Faster Pricing of Convertible Bonds

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CFA考试一级章节练习题精选0329-53(附详解)

CFA考试一级章节练习题精选0329-53（附详解）1、An analyst does research about moneyness of stock options.With respect to stockoptions, the potential for an infinite loss exists for an investor who:【单选题】A.sells a put option.B.buys a put option.C.sells a call option.正确答案:C答案解析:卖出一个看涨期权，从理论上来讲，当股票价格上升无穷大时，该卖方的损失也会无穷大；而卖出一个看跌期权，因为股票价格最低也就跌到零，所以该卖方的损失是有限的。

对于看涨期权和看跌期权的买方来讲，当不考虑期权成本时，不会发生亏损。

2、An investor who holds a long position in a futures contract will most likely receive a margin call if the ending balance in his margin account falls below the:【单选题】A.variation margin.B.initial margin requirement.C.maintenance margin requirement.正确答案:C答案解析:A margin call is due whenever the ending balance in the margin account falls below the maintenance margin requirement. 2014 CFA Level I"Futures Markets and Contracts," by Don M. ChanceSection 33、Which of the following statements best describes changes in the value of a long forward positionduring its life?【单选题】A.As interest rates go down, the value of the position goes up.B.As the time to maturity goes down, the value of the position goes up.C.As the price of the underlying goes up, the value of the position goes up.正确答案:C答案解析:Given the formula for the value of a forward contract:it follows that the value of the contract goes up as the price of the underlying goes up.CFA Level I"Basics of Derivative Pricing and Valuation, Don M. Chance, CFASection 3.1.34、Which of these is best classified as a forward commitment?【单选题】A.A swap agreementB.A convertible bondC.An asset-backed security正确答案:A答案解析:2010 Modular Level I, Vol. 6, pp. 7-10Study Session 17-67-bDefine a forward commitment and a contingent claimA swap agreement is equivalent to a series of forward agreements, which are described as forward commitments.5、An analyst does research about option moneyness.An investor paid $5 for a putoption that was in-the-money $3.If the price of the underlying was $59 at thetime the investor purchased the put option, the exercise price of that put optionwas closest to :【单选题】A.$51B.$56C.$62正确答案:C答案解析:因为是看跌期权，只有当前价格低于行权价格，该看跌期权才是价内的，并且与期权成本无关。

Simulation-Based Pricing of Convertible Bonds

Simulation-Based Pricing of Convertible BondsManuel Ammann a,Axel Kind a,∗,Christian Wilde ba Swiss Institute of Banking and Finance,University of St.Gallen,Rosenbergstrasse52,9000St.Gallen,Switzerlandb Department of Finance,Goethe University Frankfurt,60054Frankfurt,Germanyforthcoming in the Journal of Empirical FinanceAbstractWe propose and empirically investigate a pricing model for convertible bonds based on Monte Carlo simulation.The method uses parametric representations of the early ex-ercise decisions and consists of two stages.Pricing convertible bonds with the proposedMonte Carlo approach allows us to better capture both the dynamics of the underlyingstate variables and the rich set of real-world convertible bond speciﬁcations.Further-more,using the simulation model proposed,we present an empirical pricing study of theUS market,using32convertible bonds and69months of daily market prices.Our resultsdo not conﬁrm the evidence of previous studies that market prices of convertible bondsare on average lower than prices generated by a theoretical model.Similarly,our studyis not supportive of a strong positive relationship between moneyness and mean pricingerror,as argued in the literature.JEL codes:G13,G15Keywords:Convertible bonds,pricing,American options,Monte Carlo simulationThis project was supported by the Swiss National Science Foundation.We are grateful for comments of Giovanni Barone-Adesi,Murray Carlson,Robert Engle,Stephen Figlewski,Fabio Mercurio,Suresh Sun-daresan,Ingo Walter,Heinz Zimmermann,and participants of the Northern Finance Association Conference in Banff,Canada,the Quantitative Methods in Finance Conference in Cairns,Australia,the Australasian Finance and Banking Conference in Sydney,Australia,the German Finance Association Conference in Augsburg,Ger-many,and of Research Seminars at WHU in Koblenz,Germany,University of Z¨u rich,Switzerland,University of Konstanz,Germany,and Goethe University in Frankfurt,Germany.We thank Mace Advisers for providing access to the Mace Advisers convertible bond database.We also thank Zeno D¨u rr,Mark Evans,and Peter Hall for their assistance in obtaining the data and for helpful discussions.∗Corresponding author.Tel.:+41712247090;fax:+41712247088.Email addresses:manuel.ammann@unisg.ch(Manuel Ammann),axel.kind@unisg.ch(Axel Kind),and wilde@ﬁnance.uni-frankfurt.de(Christian Wilde).1Simulation-Based Pricing of Convertible BondsAbstractWe propose and empirically study a pricing model for convertible bonds based on Monte Carlo simu-lation.The method uses parametric representations of the early exercise decisions and consists of two stages.Pricing convertible bonds with the proposed Monte Carlo approach allows us to better capture both the dynamics of the underlying state variables and the rich set of real-world convertible bond spec-iﬁcations.Furthermore,using the simulation model proposed,we present an empirical pricing study of the US market,using32convertible bonds and69months of daily market prices.Our results do not conﬁrm the evidence of previous studies that market prices of convertible bonds are on average lower than prices generated by a theoretical model.Similarly,our study is not supportive of a strong positive relationship between moneyness and mean pricing error,as argued in the literature.1.IntroductionTo raise capital onﬁnancial markets,companies may choose among three major asset classes:equity, bonds,and hybrid instruments,such as convertible bonds.While issues arising from valuing equity and bonds are extensively studied by researchers in academia and industry,fewer articles focus on convertible bonds.This is surprising as convertible bonds cannot simply be considered as a combination of equity and bonds but present their own speciﬁc pricing challenges.As hybrid instruments,convertible bonds are difﬁcult to value because they depend on variables related to the underlying stock(price dynamics),theﬁxed income part(interest rates and credit risk), and the interaction between these components.Embedded options,such as conversion,call,and put provisions often are restricted to certain periods,may vary over time,and are subject to additional path-dependent features of the state variables.Sometimes,individual convertible bonds contain innovative, pricing-relevant speciﬁcations that requireﬂexible valuation models.The purpose of this study is to present a pricing model based on Monte Carlo Simulation that can deal with these valuation challenges.2We implement this model and use it to perform theﬁrst simulation-based pricing study of the US convertible-bond market that accounts for early-exercise features.Theoretical research on convertible bond pricing can be divided into three branches.Theﬁrst pricing approach impliesﬁnding a closed-form solution to the valuation equation.It was initiated by Ingersoll(1977a),who applies the contingent claims approach to the valuation of convertible bonds. In this valuation model,the convertible-bond price depends on theﬁrm value as the underlying state variable.More recently,Lewis(1991)develops a formula for convertible bonds that accounts for more complex capital structures,i.e.multiple issues.B¨u hler and Koziol(2002)focus on the possibility of non-block-constrained conversion and develop pricing formulas for simple convertible bonds.While very fast in computation,closed-form solutions are not suitable for empirical studies because they fail to account for a number of real-world speciﬁcations.1Especially,dividends and coupon payments are often modeled continuously rather than discretely,early-exercise features are omitted,and path-dependent features are excluded.The second pricing approach values convertible bonds numerically,using numerical partial dif-ferential equation mercially available models for pricing convertible bonds,such as Bloomberg OVCV,Monis,and SunGard TrueCalcTM Convertible,belong to this category.Theﬁrst theoretical model was introduced by Brennan and Schwartz(1977)who apply aﬁrm-value approach and aﬁnite-difference method for the pricing task.Brennan and Schwartz(1980)extend their pricing method by including stochastic interest rates.However,they conclude that the effect of a stochastic term structure on convertible-bond prices is so small that it can be neglected for empirical purposes. McConnell and Schwartz(1986)develop a pricing model based on aﬁnite-difference method with the stock price as stochastic variable.To account for credit risk,they use an interest rate augmented by a constant credit spread.Since the credit risk of a convertible bond varies with respect to its mon-eyness,Bardhan et al.(1993)and Tsiveriotis and Fernandes(1998)propose an approach that splits the value of a convertible bond into a stock component and a straight bond component.Ammann et. al.(2003)extend this approach by accounting for call features with various trigger conditions.Also Hung and Wang(2002)propose a tree-based model that accounts for both stochastic interest rates and1Ammann and Seiz(2006)show that in the case of mandatory convertible bonds,pricing and hedging in closed-form is rather accurate.However,this is due to the simpler payoff structure of mandatory convertible bonds.3default probabilities but looses its recombining property.A further tree-based model is presented by Carayannopoulos and Kalimipalli(2003),who use a trinomial tree and incorporates the reduced-form Dufﬁe and Singleton(1999)credit-risk model.Similar credit-risk approaches are followed by Davis and Lishka(1999),Takahashi et al.(2001),and Ayache et al.(2003),who explicitly allow for non-zero recovery rates.To sum up,among numerical partial differential equation approaches,there are both binomial/trinomial trees(e.g.Takahashi et al.,2001,Ammann et al.,2003,and Carayannopoulos and Kalimipalli,2003),ﬁnite difference(e.g.Brennan and Schwartz,1980,Ayache et al.,2003,and An-dersen and Buffum,2004),andﬁnite element methods(e.g.Barone-Adesi et al.,2003).Some of the proposed models provide sophisticated pricing and calibration solutions.Unfortunately,in the face of practical problems related to real convertible-bond speciﬁcations and limited data availability,the pro-posed approaches turn out to be practicable only in very few cases.For instance,Andersen and Buffum (2004)require for their calibration price series of several options and liquid straight bonds-a situation that is almost never given for typical convertible bond issuers.Finally,numerical partial differential equation approaches have to deal with some general challenges:computing time grows exponentially with the number of state variables,path dependencies cannot be incorporated easily,and theﬂexibility in modeling the underlying state variables is low.The third class of convertible bond pricing methods uses Monte Carlo Simulation and may over-come many of the drawbacks of numerical partial differential equation approaches.Monte Carlo Sim-ulation is very well suitable for modeling discrete coupon and dividend payments,for including more realistic dynamics of the underlying state variables,and for taking into account path-dependent call features.Typically,path dependencies arise from the fact that early redemption may only be allowed when the stock price exceeds a certain level for a pre-speciﬁed number of days in a pre-speciﬁed pe-riod,usually at least20out of the last30trading days.Finally,the relationship between the number of state variables and computing time is almost linear in our Monte Carlo framework and this can become advantageous when multiple state variables need to be modeled.Thus,the proposed model has a high degree ofﬂexibility and is friendly with respect to future extensions.Despite all the natural advantages of the Monte Carlo approach,pricing American-style options such as those present in convertible bonds within a Monte Carlo pricing framework is a demanding task.In recent years,a considerable number4of important articles have addressed the problem of pricing American-style options2by using a combi-nation of Monte Carlo Simulation and dynamic programming.Bossaerts(1989),Li and Zhang(1996), Grant et al.(1996),Andersen(2000),and Garc´ıa(2003)represent the early exercise rule via aﬁnite number of parameters.The optimal exercise strategy and hence the price of the American-style option is obtained by maximizing the value of the option over the parameter space.Carri`e re(1996),Tsit-siklis and Van Roy(1999),Longstaff and Schwartz(2001),and Cl´e ment et al.(2002)apply standard backward induction and estimate the continuation value of the option by regressing future payoffs on a set of basis functions of the state variables.Tilley(1993),Barraquand and Martineau(1995),Raymar and Zwecher(1997)present methods based on backward induction that stratify the state space andﬁnd the optimal exercise decision for each subset of state variables.Broadie and Glasserman(1997)and Broadie et al.(1997)propose a method for calculating prices of American-style options with simulated trees that generate two estimates,one biased high and one biased low.Broadie and Glasserman(2004), Broadie et al.(2000),Avramidis and Hyden(1999),and Boyle et al.(2000)develop stochastic-mesh methods with different choices for mesh weights.Finally,Broadie and Cao(2003),Haugh and Ko-gan(2004),and Rogers(2002)suggest a simulation method that uses a duality approach for pricing Bermudan options.A numerical comparison of different Monte Carlo approaches is provided by Fu et al.(2001).Previous research to value convertible bonds by Monte Carlo Simulation is very limited.Buchan (1997,1998)describes the application of the parametric optimization approach of Bossaerts(1989)to convertible bonds by employing theﬁrm value as the underlying state variable and allowing for senior debt.However,in the empirical implementation,she assumes the conversion option to be European rather than American.This paper contains a theoretical and an empirical contribution.First,we propose a stock-based pricing method for convertible bonds building on the enhanced Monte Carlo Simulation method by Garc´ıa(2003).This is a two-stage method designed to cope with the Monte Carlo bias that is inher-ent in one-stage methods.The two-step simulation method may be deﬁned as a parametric approach because it uses a parametric representation for the early exercise decisions.Theﬁrst step is an opti-2In general,simulation techniques only allow for aﬁnite number of early-exercise times and hence price Bermudan options rather than continuously exercisable American options.However,for a fairly large number of early-exercise dates,the Bermudan price may serve as an approximation for the price of the American option.5mization,in which a set of Monte Carlo simulations is used to estimate parameter values representing strategies for early exercise and to generate an in-sample price.In a next valuation stage,the optimized parameter space is applied to a second set of simulated stock-price paths to determine an out-of-sample model price for the convertible bond.The actual point estimate is then obtained by averaging the in-sample and the out-of-sample estimates.The optimization method by Garc´ıa(2003)is preferred to other approaches(simulated trees,stratiﬁcation algorithms,and stochastic meshes)because it is more parsimonious in allowing for multiple exercise opportunities.While the regression method by Longstaff and Schwartz(2001)is another suitable technique,the optimization-based approach by Garc´ıa(2003) has an attractive feature for empirical studies:the optimization algorithm can be terminated once a cer-tain level of accuracy is reached.As outlined above,the simulation approach adopted in this paper has an inherent strength as it isﬂexible in incorporating the dynamics of the state variables.Furthermore, besides discrete coupon and dividend payments,the introduced method accounts for path-dependent call triggers as outlined in the offering circulars.Instead of using aﬁrm-value model,the stock price is modeled directly,as proposed by McConnell and Schwartz(1986).Whereas the process parameters of a model based on the stock price can easily be estimated with standard methods,the fact thatﬁrm values are not observable makesﬁrm-value models notoriously hard to calibrate.Since the presented method is cash-ﬂow based,credit risk can easily be incorporated by discounting the payoffs subject to credit risk with the appropriate interest rate in the spirit of Tsiveriotis and Fernandes(1998).The second contribution in this paper is an empirical analysis of the US convertible bond market. Despite the large size of international convertible bond markets,very little empirical research has been undertaken.Previous research in this area was performed by King(1986),who examines a sample of103American convertible bonds with a lattice-based method and theﬁrm-value as stochastic ing monthly price data and a convertible bond valuation model with Cox,Ingersoll,and Ross (1985)stochastic interest rates(CIR),Carayannopoulos(1996)empirically investigates30American convertible bonds for a one-year period beginning in the fourth quarter of1989.Buchan(1997)uses a simulation-based approach to implement aﬁrm-value model with a CIR term structure model for35 Japanese convertible bonds.Buchan(1998)performs a pricing study for37US convertible bonds is-sued in1994.However,the American property of convertible bonds is not accounted for in that study. Carayannopoulos and Kalimipalli(2003)investigate25US convertible bonds with a trinomial tree.6Ammann et al.(2003)investigate on a daily basis21French convertible bonds with a binomial tree using the stock price as stochastic variable.A drawback of many of those pricing studies is the small number of data points per convertible bond:Buchan(1997)tests her pricing model only for one calendar day(bonds priced per March 31,1994),King(1986)for two days(bonds priced per March31,1977,and December31,1977), Carayannopoulos(1996)for twelve days(one year of monthly data),and Carayannopoulos and Kalim-ipalli(2003)for approximately two years of monthly data.In contrast,this study covers a larger sample using69months of daily price data,ranging from May10,1996,to February12,2002and includes32 convertible bonds in the US market.The US convertible bond market is chosen for its large size and the high number of rated issues.A second drawback of the previous pricing studies is the simple modeling of the volatility of the underlying stock.This drawback is almost inherent to the lattice approaches adopted by King(1986), Carayannopoulos(1996),Carayannopoulos and Kalimipalli(2003),and Ammann et al.(2003).Al-though Buchan(1997)uses a simulation-based approach,her model does not fully exploit the potentials provided by Monte Carlo Simulation as a constant volatility is assumed for the stock dynamics.To take into account the clustering of stock volatility,we implement the model using a GARCH(1,1)speciﬁca-tion.The paper is organized as follows:First,we introduce the convertible bond pricing model that will be applied in the empirical investigation.Second,we describe the data set and present the speciﬁc characteristics of the convertible bonds examined.Third,we discuss the empirical methodology applied when implementing the model.Finally,the empirical study compares theoretical model prices with observed market prices and analyzes the results.2.Pricing Convertible Bonds with Monte Carlo Simulation2.1.The American Option Pricing Problem for Convertible BondsA standard,plain-vanilla convertible bond is a bond that additionally offers the investor the option to exchange it for a predetermined number of stocks during a certain,predeﬁned period of time.The7bond usually offers regular coupon payments and,in case it is kept alive,is redeemed at the time of maturity T with a pre-speciﬁed amountκN,where N is the face value of the convertible bond andκis theﬁnal redemption ratio in percentage points of the face value.Althoughκis equal to one for most convertibles,some issues are redeemed at premium withκlarger than one.Let us consider time discretely with daily frequency,i.e.that time t belongs to aﬁnite set,t∈[0,1,...T],where t=0 indicates today,and t=T the day of contractual maturity.In the case of conversion,the investor receives n t S t,where the conversion ratio n t is the number of stocks the bond can be exchanged for,and S t is the equity price(underlying)at time t.If the underlying stock differs from that of the issuingﬁrm, the instrument is commonly called an ually,convertible bonds additionally contain a call option,allowing the issuer to demand premature redemption in exchange for the call price K t applicable at time t.The issuer is obliged to announce his intention to call a certain period in advance, referred to as the call notice period.If the convertible bond is called,the investor may want to exercise his conversion option at any time during the call notice period to receive the conversion value instead of the call price.Additionally,a putability feature is sometimes present.This entitles the investor to force the issuingﬁrm to prematurely repurchase the convertible bonds for a certain predeﬁned price P t.All these embedded options may be restricted to certain periods of time or speciﬁc dates.To facilitate the formal exposition,we introduce three time sets,Ωconv,Ωcall andΩput,that describe the dates at which the corresponding option is exercisable.Typically,theﬁrst possible conversion date precedes theﬁrst call opportunity and the last conversion opportunity is at maturity.Thus,the payoff of a convertible bond depends on whether and when the investor and the issuer decide to exercise their options and trigger the termination of the convertible bond.Letτ∗be the optimal stopping time,i.e.the time at which it is optimal for either the issuer or the investor to terminate the convertible bond.Hereby,the investor maximizes the value of the convertible bond whereas the issuer acts in the opposite way.The resulting action may either be conversion,a call,forced conversion, or regular redemption when the bond matures.Formally,the optimal stopping time of the convertible bond is deﬁned asτ∗=min{t:p(X t,t)=0},where p(X t,t)is the payoff resulting from the convertible bond in state X t at time t,given the optimal option-exercise behavior of both investor and issuer.[INSERT TABLE1AROUND HERE]8The alternatives presented in Table1stand for all events that will cause the convertible bond to be terminated and reﬂect boundary conditions that impede arbitrage opportunities.Besides when reaching maturity,the convertible bond can be ended by a conversion into stock,by a call,or by a put.The optimal exercise decision critically depends on the value of continuation V t,i.e.the value of the con-vertible bond if it is not exercised immediately.While the investor will convert(put)the bond as soon as n t S t>V t(P t>V t)for t∈Ωconv(t∈Ωput),the issuer will call the convertible as soon as V t>K t for t∈Ωcall.Thus,at each point in time,both investor and issuer decide whether they want to exercise their option or not and this decision is dependent on the continuation value.In the case of a call,the investor will convert the bond if the conversion value is above the call price(forced conversion),otherwise he will prefer to have it redeemed.The entries Condition and Time restrictions in Table1have to be read line by line,i.e.the condition in the second column of the table is checked only if the corresponding time restriction on the same line of the following(third)column is satisﬁed.Besides to certain pre-deﬁned times,the possibility to call the convertible bond may be restricted by certain conditions to be satisﬁed,e.g.that the conversion value exceeds a pre-speciﬁed call trigger.The investor will make use of the option to put the convertible bond when the value of continuation falls below the put price.It follows that the convertible bond will be kept alive as long as max(n t S t;P t)≤V t≤K t,i.e.that neither the investor nor the issuer will execute their options and cause the convertible bond to terminate.In addition to the payoff at the time of termination,the investor receives from his convertible bond investment all coupon payments that occurred prior to this date.Formally,the function h(Xτ∗,τ∗) represents the payoff from a convertible bond with embedded call option in state Xτ∗and at timeτ∗:h(Xτ∗,τ∗)=p(Xτ∗,τ∗)+c(τ∗)(1)where p(Xτ∗,τ∗)is the payoff from the convertible bond at the optimal time of terminationτ∗and c(τ∗)is the present value at timeτ∗of all coupon payments accumulated during the existence of the bond,i.e.beforeτ∗.As will be seen later,whether c(τ∗)contains also accrued interest payments is an empirical matter that depends on the speciﬁcation of the individual convertible bond.The price of a convertible bond can be obtained by discounting all future cashﬂows under the risk-neutral measure.Thus,valuing convertible bonds implies determining9V0=E Qe−∑τ∗−1t=0r(X t,t)h(Xτ∗,τ∗),(2)where V0is the current value of the convertible bond,τ∗is the optimal stopping time taking values in theﬁnite set{0,1,...,T},the function h(Xτ∗,τ∗)represents the payoff from a convertible bond with embedded call option in state Xτ∗and at timeτ∗,and the expectation E Q[·]is taken with respect to the equivalent Martingale measure Q deﬁned using the riskless security as the numeraire.r(X t,t)is the interest rate between time t and t+1in state X t that is applicable for discounting cashﬂows from time t+1to time t.2.2.Characterizing the Optimal Exercise DecisionBefore maturity,the optimal exercise strategy implies comparing the value of immediate exercise with the value from continuing,i.e.not exercising this period.The crucial step implies determining the conditional expected value of continuation V t.Formally,the value at a future time t of a convertible bond that is not exercised immediately,but held for one more period,is given byV t=E Qe−∑τ∗−1s=tr(X s,s)h(Xτ∗,τ∗)|F t(3)whereτ∗>t and F t represents the information available at time t.The continuation value V t can be expressed as a function of the state variables and time.In partic-ular,for convertible bonds,there is a monotonous relation between V t and the state variables.3Hence, for obtaining a full description of any economically meaningful option-exercise behavior,it is sufﬁcient to deﬁne for each embedded option only one exercise boundary Z conv,Z call,and Z put for the conversion, call,and put option,respectively.For each option,the exercise boundary separates the exercise-region from the non-exercise region.The exercise boundaries describe the combined values of state variables for which investor and issuer are indifferent between exercising their options or not.For q state vari-ables,the boundaries Z conv,Z call,and Z put can be viewed as functions that associate to any date t and3For example,Vt is monotonically increasing in the stock price S,with0<dV t/dS<n,given speciﬁcvalues for the other state variables.Therefore,for every embedded option,there is at most one S for which the continuation value is equal to the respective option payoff if exercised(K t,n t S t,and P t).10any values of q−1state variables critical values for the remaining state variable q that trigger the ex-ercise of the respective option.Z convtdenotes,for a speciﬁc date t∈Ωconv,the value of state variable qfor which V t=n t S t.Similarly,Z calltdenotes,for a speciﬁc date t∈Ωcall,the value of state variable q for which V t=K t and Z put t denotes,for a speciﬁc date t∈Ωput,the value of state variable q for which V t=P t.In the case where the stock price S is the only state variable,it is optimal to exercise the optionswhenever S t>Z convt ,S t>Z callt,and S t<Z put t,where Z convt,Z callt,and Z put t are scalars.As describedin Appendix A,for the numerical implementation,the exercise boundaries Z conv,Z call,and Z put are approximated by parametric functions G conv(t;θconv),G call(t;θcall),and G put(t;θput)with parameter setsθconv,θcall,andθput.2.3.Simulation MethodologyThe pricing algorithm consists of two stages,an optimization stage and a valuation stage.In theﬁrst stage,the optimal exercise strategy of the investor and the issuer is estimated using aﬁrst set of sim-ulated paths for the state variables.The parameter setsθiss andθinv govern the exercise behavior,or exercise strategy,of the issuer and investor,respectively.The exercise behavior of the issuer con-cerns solely the call option so that we can write without loss of generalityθiss=θcall.Since the investor’s exercise behavior is related to both the conversion and the put option,we can convenientlywriteθinv=θ convθ put.These exercise strategies determine the time of termination,or stopping time,τ,of the convertible bond.Hence,the value of the convertible bond given certain exercise strategies can be calculated by averaging the discounted payoffs of all simulation paths:V0(θinv,θiss)=1NN∑i=1e−∑τi(θinv,θiss)−1t=0r(X t,t)hX iτi(θinv,θiss),τi(θinv,θiss),(4)where X t are realizations of the simulated state variables and N is the number of simulation paths.Toﬁnd the optimal conversion strategy,given aﬁxed call strategy,the initially chosen parameters encoding the put and the conversion strategy are altered until the algorithmﬁnds a maximum for the convertible bond price:11θinv =arg θinv max V 0 θinv , θiss ,(5)where θinv indicates an estimate of the optimal exercise strategy of the investor.Subsequently,these parameters are applied to ﬁnd a call strategy that minimizes the convertible-bond price:θiss =arg θiss min V 0 θinv ,θiss .(6)To determine the ﬁnal exercise strategy,this procedure is applied iteratively until the optimal pa-rameters are obtained and a predeﬁned accuracy is reached.The relevant stopping times τ∗i θinv , θiss for each path i and the corresponding payoffs h X τ∗i,τ∗i for valuing a convertible bond are obtained by applying these optimized exercise rules to the simulated paths.Thus,as a result of this procedure,we obtain estimates of the optimal exercise strategies as well as an in-sample estimate of the price of the convertible bond.In the second stage,the optimized exercise strategies from the ﬁrst stage are applied on a second set of simulated paths of the state variables to determine the out-of-sample value of the convertible bond.The ﬁnal point estimate is the average of the in-and out-of-sample estimates.While numerical experiments show that both the in-sample and the out-of-sample estimates converge to the true price of the convertible bond as the number of simulation paths increases,averaging the two results generates a more accurate point estimate.Figure 1presents a comparison of exercise boundaries obtained by a 6000-step binomial tree and the simulation-based model.For the sake of comparison the convertible bond only has only features that can be easily addressed within a standard binomial tree model.We investigate a simple case with the stock price as the only state variable and constant interest rates.As can be seen in the plots,the main features of the exercise boundaries are captured by the simulation model.The fact that the conversion boundary is lower in the simulation model can be easily explained.As long as the conversion boundary is higher than the call boundary,its exact position does not affect the price of the convertible bond.Thus,if during any step of the maximization procedure (cfr.equation (5))the optimizer sets the con-version boundary in an arbitrary position above the call boundary,no change of the parameters θconv will increase the price of the convertible and the current position of the conversion boundary will be12。

罗斯公司理财第九版原版书课后习题Cha24

(after conversion) exceed the company’s interest payment. See Louis H. Ederington, Gary L. Caton, and Cynthia J. Campbell, “To Call or Not to Call Convertible Debt,” Financial Management (Spring 1997).Summary and Conclusions1. A warrant gives the holder the right to buy shares of common stock at an exercise price for agiven period. Typically, warrants are issued in a package with privately placed bonds. Afterwards, they become detached and trade separately.2. A convertible bond is a combination of a straight bond and a call option. The holder can give upthe bond in exchange for shares of stock.3. Convertible bonds and warrants are like call options. However, there are some importantdifferences:1. Warrants and convertible securities are issued by corporations. Call options are tradedbetween individual investors.1. Warrants are usually issued privately and are combined with a bond. In most cases,the warrants can be detached immediately after the issue. In some cases, warrants areissued with preferred stock, with common stock, or in executive compensationprograms.2. Convertibles are usually bonds that can be converted into common stock.3. Call options are sold separately by individual investors (called writers of call options).2. Warrants and call options are exercised for cash. The holder of a warrant gives thecompany cash and receives new shares of the company’s stock. The holder of a call optiongives another individual cash in exchange for shares of stock. When someone converts abond, it is exchanged for common stock. As a consequence, bonds with warrants andconvertible bonds have different effects on corporate cash flow and capital structure.3. Warrants and convertibles cause dilution to the existing shareholders. When warrants areexercised and convertible bonds converted, the company must issue new shares of commonstock. The percentage ownership of the existing shareholders will decline. New shares are notissued when call options are exercised.4. Many arguments, both plausible and implausible, are given for issuing convertible bonds andbonds with warrants. One plausible rationale for such bonds has to do with risk. Convertibles and bonds with warrants are associated with risky companies. Lenders can do several things to protect themselves from high-risk companies:1. They can require high yields.2. They can lend less or not at all to firms whose risk is difficult to assess.3. They can impose severe restrictions on such debt.Another useful way to protect against risk is to issue bonds with equity kickers. This gives the lenders the chance to benefit from risks and reduces the conflicts between bondholders and stockholders concerning risk.5. A certain puzzle particularly vexes financial researchers: Convertible bonds usually have callprovisions. Companies appear to delay calling convertibles until the conversion value greatly exceeds the call price. From the shareholders’ standpoint, the optimal call policy would be to call the convertibles when the conversion value equals the call price.Concept Questions1. Warrants and Options What is the primary difference between a warrant and a traded calloption?2. Warrants Explain the following limits on the prices of warrants:1. If the stock price is below the exercise price of the warrant, the lower bound on the priceof a warrant is zero.2. If the stock price is above the exercise price of the warrant, the lower bound on the priceof a warrant is the difference between the stock price and the exercise price.3. An upper bound on the price of any warrant is the current value of the firm’s stock.3. Convertible Bonds and Stock Volatility Suppose you are evaluating a callable, convertiblebond. If the stock price volatility increases, how will this affect the price of the bond?4. Convertible Bond Value What happens to the price of a convertible bond if interest ratesincrease?5. Dilution What is dilution, and why does it occur when warrants are exercised?6. Warrants and Convertibles What is wrong with the simple view that it is cheaper to issue abond with a warrant or a convertible feature because the required coupon is lower?7. Warrants and Convertibles Why do firms issue convertible bonds and bonds with warrants?8. Convertible Bonds Why will convertible bonds not be voluntarily converted to stock beforeexpiration?9. Convertible Bonds When should a firm force conversion of convertibles? Why?10. Warrant Valuation A warrant with six months until expiration entitles its owner to buy 10shares of the issuing firm’s common stock for an exercise price of $31 per share. If the current market price of the stock is $15 per share, will the warrant be worthless?Question and Problems connect™BASIC (Question 1–9)1. Conversion Price A convertible bond has a conversion ratio of 18.4. What is the conversionprice?2. Conversion Ratio A convertible bond has a conversion price of $70.26. What is the conversionratio of the bond?3. Conversion Premium Eckely, Inc., recently issued bonds with a conversion ratio of 12.8. Ifthe stock price at the bond issue date was $61.18, what was the conversion premium?4. Convertible Bonds Hannon Home Products, Inc., recently issued $2 million worth of 8 percentconvertible debentures. Each convertible bond has a face value of $1,000. Each convertible bond can be converted into 18.5 shares of common stock anytime before maturity. The stock price is $38.20, and the market value of each bond is $1,070.1. What is the conversion ratio?2. What is the conversion price?3. What is the conversion premium?4. What is the conversion value?5. If the stock price increases by $2, what is the new conversion value?5. Warrant Value A warrant gives its owner the right to purchase three shares of common stockat an exercise price of $41 per share. The current market price of the stock is $47. What is the minimum value of the warrant?6. Convertible Bond Value An analyst has recently informed you that at the issuance of acompany’s convertible bonds, one of the two following sets of relationships existed:Assume the bonds are available for immediate conversion. Which of the two scenarios do you believe is more likely? Why?7. Convertible Bond Value Sportime Fitness Center, Inc., issued convertible bonds with aconversion price of $34. The bonds are available for immediate conversion. The current price of the company’s common stock is $29 per share. The current market price of the convertible bonds is $990. The convertible bonds’ straight value is not known.1. What is the minimum price for the convertible bonds?2. Explain the difference between the current market price of each convertible bond and thevalue of the common stock into which it can be immediately converted.8. Convertible Bonds You own a callable, convertible bond with a conversion ratio of 21.5. Thestock is currently selling for $52 per share. The issuer of the bond has announced a call at a call price of $110. What are your options here? What should you do?9. Warrant Value General Modems has five-year warrants that currently trade in the openmarket. Each warrant gives its owner the right to purchase one share of common stock for an exercise price of $55.1. Suppose the stock is currently trading for $51 per share. What is the lower limit on theprice of the warrant? What is the upper limit?2. Suppose the stock is currently trading for $58 per share. What is the lower limit on theprice of the warrant? What is the upper limit?10. Convertible Bonds Bernanke Corp. has just issued a 30-year callable, convertible bond with acoupon rate of 6 percent annual coupon payments. The bond has a conversion price of $130. The company’s stock is selling for $26 per share. The owner of the bond will be forced to convert if the bond’s conversion value is ever greater than or equal to $1,100. The required return on an otherwise identical nonconvertible bond is 11 percent.INTERMEDIATE (Questions 10–13)1. What is the minimum value of the bond?2. If the stock price were to grow by 13 percent per year forever, how long would it take forthe bond’s conversion value to exceed $1,100?11. Convertible Bonds Rob Stevens is the chief executive officer of Isner Construction, Inc., andowns 750,000 shares of stock. The company currently has 5 million shares of stock and convertible bonds with a face value of $30 million outstanding. The convertible bonds have a conversion price of $34, and the stock is currently selling for $40.1. What percentage of the firm’s common stock does Mr. Stevens own?2. If the company decides to call the convertible bonds and force conversion, whatpercentage of the firm’s common stock will Mr. Stevens own? He does not own any convertible bonds.12. Warrants Survivor, Inc., an all-equity firm, has eight shares of stock outstanding. Yesterday,the firm’s assets consisted of nine ounces of platinum, currently worth $850 per ounce. Today, the company issued Ms. Wu a warrant for its fair value of $850. The warrant gives Ms. Wu the right to buy a single share of the firm’s stock for $1,000 and can be exercised only on its expiration date one year from today. The firm used the proceeds from the issuance to immediately purchase an additional ounce of platinum.1. What was the price of a single share of stock before the warrant was issued?2. What was the price of a single share of stock immediately after the warrant was issued?3. Suppose platinum is selling for $975 per ounce on the warrant’s expiration date in oneyear. What will be the value of a single share of stock on the warrant’s expiration date?13. Warrants The capital structure of Ricketti Enterprises, Inc., consists of 15 million shares ofcommon stock and 1 million warrants. Each warrant gives its owner the right to purchase one share of common stock for an exercise price of $19. The current stock price is $25, and each warrant is worth $7. What is the new stock price if all warrant holders decide to exercise today?CHALLENGE (Questions 14–16)14. Convertible Calculations You have been hired to value a new 25-year callable, convertiblebond. The bond has a 6.80 percent coupon rate, payable annually. The conversion price is $150, and the stock currently sells for $35.50. The stock price is expected to grow at 12 percent per year. The bond is callable at $1,150; but based on prior experience, it won’t be called unless the conversion value is $1,250. The required return on this bond is 9 percent. What value would you assign to this bond?15. Warrant Value Superior Clamps, Inc., has a capital structure consisting of 6 million shares ofcommon stock and 750,000 warrants. Each warrant gives its owner the right to purchase one share of newly issued common stock for an exercise price of $20. The warrants are European and will expire one year from today. The market value of the company’s assets is $105 million, and the annual variance of the returns on the firm’s assets is .15. Treasury bills that mature in one year yield a continuously compounded interest rate of 7 percent. The company does not pay a dividend.Use the Black–Scholes model to determine the value of a single warrant.16. Warrant Value Omega Airline’s capital structure consists of 3.2 million shares of common stockand zero coupon bonds with a face value of $18 million that mature in six months. The firm just announced that it will issue warrants with an exercise price of $75 and six months until expiration to raise the funds to pay off its maturing debt. Each warrant can be exercised only at expiration and gives its owner the right to buy a single newly issued share of common stock. The firm will place the proceeds from the warrant issue immediately into Treasury bills. The market value balance sheet shows that the firm will have assets worth $210 million after the announcement. The company does not pay dividends. The standard deviation of the returns on the firm’s assets is 50 percent, and Treasury bills with a six-month maturity yield 6 percent. How many warrants must the company issue today to be able to use the proceeds from the sale to pay off the firm’s debt obligation in six months?Mini Case: S&S Air’s Convertible BondChris Guthrie was recently hired by S&S Air, Inc., to assist the company with its short-term financial planning and to evaluate the company’s performance. Chris graduated from college five years ago with a finance degree. He has been employed in the finance department of a Fortune 500 company since then.S&S Air was founded 10 years ago by two friends, Mark Sexton and Todd Story. The company has manufactured and sold light airplanes over this period, and the company’s products have received high reviews for safety and reliability. The company has a niche market in that it sells primarily to individuals who own and fly their own airplanes. The company has two models: The Birdie, which sells for $53,000, and the Eagle, which sells for $78,000.S&S Air is not publicly traded, but the company needs new funds for investment opportunities. In consultation with Tonisha Jones of underwriter Raines and Warren, Chris decided that a convertible bond issue with a 20-year maturity is the way to go. He met with the owners, Mark and Todd, and presented his analysis of the convertible bond issue. Because the company is not publicly traded, Chris looked at comparable publicly traded companies and determined that the average PE ratio for the industry is 12.5. Earnings per share for the company are $1.60. With this in mind, Chris concluded that the conversion price should be $25 per share.Several days later, Todd, Mark, and Chris met again to discuss the potential bond issue. Both Todd and Mark have researched convertible bonds and have questions for Chris. Todd begins by asking Chris if the convertible bond issue will have a lower coupon rate than a comparable bond without a conversion feature. Chris replies that to sell the bond at par value, the convertible bond issue would require a 6 percent coupon rate with a conversion value of $800, while a plain vanilla bond would have a 7 percent coupon rate. Todd nods in agreement, and he explains that the convertible bonds are a win–win form of financing. He states that if the value of the company stock does not rise above the conversion price, the company has issued debt at a cost below the market rate (6 percent instead of 7 percent). If the company’s stock does rise to the conversion value, the company has effectively issued stock at above the current value.Mark immediately disagrees, arguing that convertible bonds are a no-win form of financing. He argues that if the value of the company stock rises to $25, the company is forced to sell stock at the conversion price. This means the new shareholders (those who bought the convertible bonds) benefit from a bargain price. Put another way, if the company prospers, it would have been better to have issued straight debt so that the gains would not be shared.Chris has gone back to Tonisha for help. As Tonisha’s assistant, you’ve been asked to prepare another memo answering the following questions:1. Why do you think Chris is suggesting a conversion price of $25? Given that the company is notpublicly traded, does it even make sense to talk about a conversion price?2. What is the floor value of the S&S Air convertible bond?3. What is the conversion ratio of the bond?4. What is the conversion premium of the bond?5. What is the value of the option?6. Is there anything wrong with Todd’s argument that it is cheaper to issue a bond with aconvertible feature because the required coupon is lower?7. Is there anything wrong with Mark’s argument that a convertible bond is a bad idea because itallows new shareholders to participate in gains made by the company?8. How can you reconcile the arguments made by Todd and Mark?9. During the debate, a question comes up concerning whether the bonds should have an ordinary(not make-whole) call feature. Chris confuses everybody by stating, “The call feature lets S&S Airforce conversion, thereby minimizing the problem Mark has identified.’’ What is he talking about? Is he making sense?。

英汉国际会计准则词汇表 trados必备翻译好帮手~~~~~~

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other payablestrade and other receivablestrade discounttrade discount and rebatetrade investmenttrade liabilitiestrademarktransaction costs (financial instruments) transanction in foreign currencytransfertransfer pricetransitional liability ( defined benefit plans) transitional provisiontreasury sharestrue and fair viewtrust activitiestrust fundtrusteesultimate redemption valueunderlyingunderlying financial instrumentunderlying primary financial instrument understandabilityunearned finance incomeunguaranteed residual valueunit of production methoduniting of interestsunquotesunrealized gainunrealized lossunrealized profitunused tax creditunusual itemupstream activitesupstream productupstream transactionsuseful lifevacation payvalid expectationvaluationvariable production overheadsventurervested employee benefitsvoting rightwarrantwarrantywarranty costswarranty provisionsweighted average cost formulasweighted average cost methodwelfare planwholly-owned subsidiarywithholding taxwork in progresswork performed by the enterprises and capitalised working capitalwrite backwrite downwrite offwrite-down investories on an item by item basis writeryield企业集团加速股利会计假设会计估计会计处理，会计核算会计收益会计期间会计政策会计利润会计处理应计权责发生制，应计制应计雇员费用应计负债累计摊销额累计汇兑差额累计损益累计带薪缺勤被购方购买方购买，收买，购并购买费用活跃市场实际汇率精算假设精算损益承诺福利的精算现值承诺退休福利的精算现值精算报告精算技术精算估价精算师追加的，额外的额外对价行政费用预收款，预付款加总，汇总，总计加总价值分配，分摊备抵，折让允许选用的处理方法摊销摊销方法摊销期摊余成本金额可收回金额，可补偿金额辅助费用年度报告，年报预期未来交易反稀释分配，分拨正常交易，公平交易要价评价，评估资产产权转让联营企业归属于批准报出可供出售的平均账面金额平均汇率收益与成本的平衡资产负债表负债法银行透支基本每股收益期初基准处理方法受益方最佳估计投标保函出价票据约束性销售协议董事会奖金，红利红股奖金计划借款协议借款费用自下而上测试分支机构经纪人佣金，经纪人业务企业合并购买式企业合并业务分部回购采购分部看涨期权，买入期权可赎回的可赎回债券（利率）上限资本资本法资本资产定价模型资本承诺资本投入资本利得资本保全资本交易资本化资本化发行资本化比率结转后期未利用的税款抵扣结转后期未利用的可抵扣（应税利润额的）亏损结转后期账面金额可抵扣（应税利润额的）亏损抵前现金收付实现制现金等价物现金流量现金流量风险现金流量表现金产出单元银行存款现金流入库存现金现金流出存单会计政策变更财务状况变动借记，计入首席执行官，行政总裁，总经理资产类别归类，分类清算所期末汇率可回收性收账费用并股合并合并实体合并经营成果合并和分立的建造合同参与合并的企业佣金承诺承诺费，承约费商品合同商品期货合同以商品为基础的合同普通股可比性不加控制的可比价格法比较期间带薪缺勤补偿，报酬复合金融工具计算机软件信用风险集中对价一致性合并资产负债表合并财务报表合并集团合并收益表合并并股合并程序固定回报率建造合同施工间接费用推定义务易耗品或有事项或有资产或有承诺或有利得或有负债或有损失或有租金或有可发行股合同，合约承包商合同义务合同条款合同权利注资，出资出资，提存金控制惯例转换期权转换权转换可转换可转换债券版权总部资产区间成本成本法购买成本，收买成本，购并成本处置成本销售成本存货成本人工成本采购成本销售成本销售成本法成本回收法成本节省成本加成合同成本加成法购买成本材料成本注册费用完工尚未发生的成本对应方贷记，贷项信用便利信用风险赊销期限债权人信用可靠度累积优先股股利累积优先股货币风险货币互换货币折算差额当期和预期获利能力流动资产现行成本现行成本法现行成本财务报表现行利率短期投资流动负债当期当期工资法当期服务成本当期税金缩减顾客信赖，顾客忠诚购买日，收买日，购并日出资日报告日评估日日常活动交易性证券债务拖欠债务性工具债务性证券债务-权益比率下跌可抵扣暂时性差异违约递延法递延酬劳递延酬劳安排递延汇兑损益递延收益递延付款递延付款条件递延收入递延所得税资产递延所得税负债递延所得税设定受益计划设定提存计划可比程度交付，交割，交货；送达活期存款明确承诺提取存款应折旧金额应折旧资产折旧折旧方法折旧率终止确认（某一金融工具）终止确认（某一金融工具）衍生金融工具衍生工具开发费用开发支出开发阶段稀释每股收益稀释稀释选择权稀释性潜在普通股余额递减折旧法直接影响直接增量费用直接投资直接人工直接发直接关系可直接归属的支出解脱，解除披露披露已终止经营终止经营折价，折扣，贴水折现率处置处置收入子公司的处置处置亏本销售分派，分配销售费用，分销费用股利收益应收股利股利率股利股利政策跟单信贷下游交易，下销交易收益每股收益，每股盈利获利能力经济利益经济寿命经济业绩生效日期实际利率法实际收益率消除嵌入衍生工具雇员福利雇员福利费用期末实体权益权益资本权益计酬福利权益计酬计划权益性金融工具权益性工具股份发行权益法权益性证券估计价值评价，估价资产负债表日后事项汇率外汇管制汇兑差额汇兑损失资产交换执行待执行合同行使日行使价格现有用途，现行用途预期增长率预期价值，预期价值法结转后期的支出费用经验调整失效，满期，终止满期日，终止日说明性注释勘探风险敞口除权展期外部客户消除消除债务采掘非常项目资产负债表表内收益表表内公允表述，公允列报公允价值真实反映费，手续费伙伴子公司先进先出法筹资费用筹资成本融资收益融资租赁为交易而持有的金融资产或负债金融资产财务预算财务担保金融机构金融工具财务权益金融负债财务或财政援助财务业绩财务政策财务状况财务审阅，财务审核财务权利财务报表财务结构财务支持财务年度财务年度年初至今基础筹资活动筹资安排筹资手段产成品确定承诺确定购买合同确定销售合同财政政策固定造价合同固定制造费用固定赎回价值浮动利率，浮动汇率（利率）下限强制性交易国外业务外币外币借款外币套期外币交易国外实体汇兑损益国外经营预计寿命饶让贷款远期合同框架特许权费受让人（接受特许权人）特许权费特许人（授出特许权人）精算估价周期全额支付重大差错注资政策注资风险代客持有资金追加费用未来经济利益期货合同利得一般行政费用（财务报表中）一般披露要求一般物价水平一般购买力法通用财务报表一般工资水平地区分部持续经营商誉政府援助政府补助政府采购与资产相关的政府补助与收益相关的政府补助账面总金额融资租赁投资总额销售毛利毛利指南标题总部的费用套期会计套期有效性被套期项目套期套期工具为交易而持有持有至到期的投资租购合同历史成本历史成本制度损坏责任转移协议控股公司主合同恶性通货膨胀恶性通货膨胀经济可辨认性可辨认资产资产和负债的认定认定，辨认不重要减值减值损失资产减值推算成本，假计成本估算利率奖励租赁起始日发生率收益收益法来自联营企业的收益收益表收益表负债法所得税所得税资产所得税法所得税负债产生收益的资产（承租人）增量借款利率增量股份豁免条款间接法单个资产，个别资产单个负债，个别负债初始账面价值（终止经营的）初始披露事项初始计量初始确认保险合同保险费承保人无形资产（雇员福利计划的）利息成本合营企业中的权益利息收益附息或不附息的负债与准备利率上限利率上下限组合利率下限租约中的内含利率利率风险利率互换本金剥离中期财务报告中期内部管理结构内部组织结构内部利润内部报告分部自创商誉国际会计准则国际会计准则委员会集团内部交易存货投资活动投资企业投资投资收益投资业绩投资性房地产投资性证券投资税款抵减合营中的投资者非自愿清算股票发行已发行股本项目共同控制共同拥有合营产品合营企业合营活动合营协议共同控制资产共同控制实体共同控制景扬管辖区域，管辖范围人工租赁租赁期法律顾问律师费用法律实体法定兼并法定义务法定执行权贷款人出借方回报承租人出租人信用证平均收益率杠杆租赁负债负债法许可证许可证费，执照费许可证受让人许可协议许可证让予人人寿保险企业后进先出法逐项报告格式单列项目清算流动性流动性风险。

财务管理Convertible bond 演讲

Out-the-money
4、use for investors
Convertible bonds are usually issued offering a higher yield than obtainable on the shares into which the bonds convert. Convertible bonds are safer than prefferred or common shares for the investor Also, convertible bonds are usually less volatile than regular shares
2、Types
There are many variations of the basic structure of a convertible bond.
Vanilla convertible bonds Mandatory convertibles Contingent convertibles Exchangeables Mandatory exchangeables OCEANE
The simultaneous purchase of convertible bonds and the short sale of the same issuer's common stock is a hedge fund strategy known as convertible arbitrage Death spiral financerred stock
Reverse convertible securities Going-public bonds
SPV structures

CFA考试二级模拟试题精选0401-20(附详解)

CFA考试二级模拟试题精选0401-20(附详解）1、The normalized earnings after tax for FAMCO is closest to:【单选题】A.$32,940,000.B.$34,260,000.C.$34,860,000.正确答案:C答案解析:C is correct. The new interest level is $2,000,000 instead of $1,000,000. SG&A expenses are reduced by $1,600,000 ( = $5,400,000 – $7,000,000) to $21,400,000 by salary expense savings. Other than a calculation of a revised provision for taxes, no other changes to the income statement results in normalized earnings before tax of $58,100,000 and normalized earnings after tax of $34,860,000.2、The hypothetical Orion trade generated an approximate:【单选题】A.loss of ￡117,000.B.gain of ￡117,000.C.gain of ￡234,000.正确答案:B答案解析:B is correct. The gain on the hypothetical Orion trade is ￡117,000, calculated as follows.3、What is the value per share of High Tech stock using the discounted cash flow approach if the terminal value of High Tech is based on using the cash flow multiple method to determine terminal value?【单选题】A.$35.22.B.$40.56.C.$41.57.正确答案:B答案解析:B is correct. The estimated stock price is $40.56.4、Dobson is wondering what the consequences would be if the duration of the first stage was assumed to be 11 years instead of 8, with all the other assumptions/estimates remaining the same. Considering this change, which of the following is true?【单选题】A.In the second approach, the proportion of the total value of the stock represented byB.The total value estimated using the third approach would increase.C.正确答案:B答案解析:B is correct. If the extraordinary growth rate of 14 percent is expected to continue for a longer duration, the stock’s value would increase. Choice A is false because given that the first stage is longer (11 years instead of 8), the terminal value is being calculated at a later point in time. So, its present value would be smaller. Moreover, the first stage has more years and contributes more to the total value. Overall, the proportion contributed by the second stage would be smaller. Choice C is false because the intrinsic value of the stock would be higher and the appropriate conclusion would be that the stock would be undervalued to a greater extent based on the first approach.5、When removing the multi-factor analysis from his research report, does Grohl violate any CFA Standards?【单选题】A.No.B.Yes, because he no longer has a reasonable basis for his recommendation.C.Yes, because he is required to make full and fair disclosure of all relevant正确答案:A答案解析:A is correct. Removing the multi-factor analysis from the research report does not constitute a violation. Grohl diligently prepared the internal document according to the firm’s traditional format with a complete fundamental analysis and recommendati on—indicating diligence and a reasonable basis for his recommendation. It would be wise for Grohl to retain records of the multi-factor analysis but he need not retain the analysis in the research report to comply with Standards V(A)–Diligence and Reasonable Basis or V(C)–Record Retention.6、The divestiture technique that Lee is recommending is most likely:【单选题】A.a spin-off.B.a split-off.C.an equity carve-out.正确答案:C答案解析:C is correct. An equity carve-out involves sale of equity in a new legal entity to outsiders, and would thus result in a cash inflow for Moonbase. A spin-off or a split-off does not generate a cash flow to the firm.7、Based on Note 16, after reclassifying pension components to reflect economic income or expense, the net adjustment to profit before taxation is:【单选题】A.–€205 million.B.–€94 million.C.+€129 million.正确答案:B答案解析:B is correct. Operating income is adjusted to include only the current service costs, the interest cost component is reclassified as interest expense, and the actual return on plan assets is added as investment income. Profit before taxation adjusted for actual rather than expected return on plan assets will decrease by €94 million (205 – 299).8、The value of Position 2 is closest to:【单选题】A.–￥149,925.B.–￥150,000.C.–￥150,075.正确答案:A答案解析:A is correct. The value of Troubadour’s euro/JGB forward position is calculated as9、【单选题】A.B.C.正确答案:C答案解析:The 7-year, 7.25% convertible bond has a market price of $947 (given) and, therefore, does not qualify (as it is below par).10、Which of the following statements regarding the consolidation of WMC's Ukrainian subsidiary for the next year is least likely correct? Compared to the temporal method, the Ukrainian subsidiary's translated:【单选题】 income before translation gains or losses would be higher using the current rate method.B.Debt-to-equity ratio would be higher using the current rate method.C.Gross profit margin would be lower using the current rate method.正确答案:C答案解析:Under both the current rate and temporal methods, the revenues for the Ukrainian subsidiary would be translated using the average rate. Cost of goods sold (COGS) would be translated using the historical rate for the temporal method and the average rate for the current rate method. When a currency is depreciating, the COGS based on historical cost (temporal method) will be higher than COGS translated at the average rate (current rate method) since the average rate will incorporate the historical exchange rate and the most recent (depreciated) exchange rate, decreasing the COGS. Since translated sales are the same under both methods, gross profit and the gross profit margin will be higher under the current rate method.。

金融英语第十章答案

金融英语第十章答案Exercises of Chapter 10I. Answer the following questions in English.1.When is bond said to be selling at a premium and when is bond said to be selling at a discount?Ans: When a bond trades at a price above the face value,it is said to be selling at a premium. When a bond sells below face value, it is said to be selling at a discount.2.What is the most important source of risk for bonds in general? Ex plain.Ans: Interest rate risk is the number one source of risk to fixed-in come investors,because it's the major cause of price volatility in the bond market.3.What is the major advantage for municipal bonds?Ans: The major advantage to munis is that the returns are free from federal tax.4.What is the coupon?Ans: The coupon is the amount the bondholder will receive as inte rest payments.5.What are callable bonds?Ans: A bond that can be redeemed by the issuer prior to its maturit y. Usually a premium is paid to the bond owner when the bond is calle d. Also known as a "redeemable bond".6.How to classify fixed-income securities in general?Ans: In general, fixed-income securities are classified according to the length of timebefore maturity7.What are zero-coupon bonds?Ans: This is a type of bond that makes no coupon payments but instead is issued at aconsiderable discount to par value.8.What do bond brokers do for investors?Ans: A full service or discount brokerageⅡ. Fill in the each blank with an appropriate word o r expression.l. Interest Rate Risk is the number one source of risk to fixed-incom e investors,because it's the ( major )cause of price volatility in the bond market.2.In the ( case )of bonds, interest rate risk translates ( into ) marketrisk: The behavior of interest rate, in general, affects all bond s and cuts( across ) all sectors of the market-even the U.S. Treasury mar ket.3. When market interest rates rise, bond prices fall, and vice ver sa. And asinterest rates become more volatile,( so ) do bond prices.4. This is a type of bond that makes no coupon payments but( ins tead )isissued at a considerable discount to par value. For example, let's say a zero-coupon bond with a $1 000 par value and 10 years to maturity is( trading )at $ 600; you'd be paying $ 600 ( today )for a bond that wil l be worth$1 000 in 10 years.5. Bonds have a ( number )of characteristics of which youneed to be aware.All of these factors play a role in determining the value of a b ond and theextent to( which )it fits in your portfolio.6. In general, fixed-income securities are classified( according to )the length of timebefore maturity. These are the three main categories.III. Translate the following sentences into English.l.债券买卖是指交易双方以约定的价格买卖一定金额的债券并在规定的清算时间内办理债券款项交割的交易方式。

含权债估值方法

含权债估值方法Valuation of convertible bonds is a complex process that involves various methods, each with its pros and cons. The traditional method for valuing convertible bonds is the "straight bond method," which values the bond as if it were a straight bond without the conversion option. 这种方法简单易行，但并没有充分考虑到债券转换权的价值。

另一种方法是期权定价方法，该方法通过计算债券中的隐含期权价值来估值。

这种方法考虑了债券的转换特性，但对于复杂的债券结构可能会产生较大的误差。

The Black-Scholes model is a widely used option pricing model that could be applied to value the embedded option in the convertible bond. It considers various factors such as the underlying stock price, the option strike price, the risk-free rate, the stock volatility, and the time to maturity. 黑-施格尔模型通过对权证定价的变量及影响因素进行建模来进行转债的估值。

然而，这种模型并不能完全适用于所有类型的转债，因为它假设了固定的利率和波动率，这与实际情况可能存在一定偏差。

Another commonly used method for valuing convertible bonds is the "market price method", which involves comparing the market valueof the convertible bond to the market value of its underlying stock and its straight bond counterpart. 这种方法较为直接，但可能无法反映出转债中的隐含期权价值。

可转换债券的结构特点与无套利定价模型(doc 47页)

可转换债券的结构特点与无套利定价模型(doc 47页)导言可转换债券是一种极其复杂的信用衍生产品。

除了一般的债权以外，它还包含着很多的期权，包括转股权、回售权、赎回权和转股价调低权。

条款的复杂性决定了可转债定价的复杂性。

其定价方法主要是依据布莱克一斯科尔斯期权定价公式。

费雪·布莱克(Fisher.Black)和迈伦·休斯(Myron S.Scholes )提出著名的以他们的名字命名的定价公式，即布莱克一斯科尔斯期权定价公式(Black-Scholes Option Pricing Model)。

1975年期权交易商开始使用这一公式，通过设计特别的计算机程序进行运算，为期权定价并规避风险。

目前，世界成千上万的投资者和交易商每天都用这一公式进行股票期权定价，并用于计算可转换债券等复杂的金融衍生工具，该公式无论在理论上还是实践上都为金融衍生市场发展提供了有力的工具。

可转换公司债券是在国际资本市场风行数十年的金融产品，而目前在我国资本市场上尚属新颖而相对陌生的筹资工具。

对比配股和增发两种融资方式，可转换债券具有融资成本低、集资力度大、偿债压力小、股本扩张适度和可溢价转股等多项优势，作为除配股和增发以外可用来筹集资金的第三种方式，很受上市公司的欢迎。

然而国际市场的经验表明，对于包括可转换债券在内的各种复杂衍生证券，只有市场参与者普遍认同其定价分析方法，该衍生证券才能在市场上蓬勃发展，正是基于这一考虑，我选定了可转换债券定价理论作为我的论文研究方向。

可转换债券定价理论属于金融产品定价理论中的一个重要部分，其历史源远流长，学者们早在1900年就己开始研究，包括萨缪尔森等人都进行过不懈的努力，金融产品定价理论中居主要地位的有内在价值决定论、价格决定论、资本资产定价模型、因素模型、套利定价模型，这些理论都曾被某种程度的用来指导可转换债券定价，但效果均不理想。

由于可转换债券含有期权，直到1973年以前，学者们基本上都采用这样的方法，即先确定到期日期权的预期价值，再通过贴现倒推出发行时期权的价值。

中级财务会计英文课件 (20)

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Employee Share Purchase Plans
Permit employees to buy shares directly from their employer. Usually the plan is considered compensatory, and compensation expense is recorded. Employees may buy 100 shares of no par stock for $8.50 per share. The current market price is $10.00. The $1.50 discount is recorded as compensation expense:
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Basic Earnings Per Share
Simple Capital Structure
(Basic EPS)
Net income (after tax) – Preferred dividends* Weighted average outstanding common stock
Cash (100 × $8.50) 850 Compensation expense (100 × $1.50) 150 Common stock (100 × $10.00) 1,000
Market value
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Earnings Per Share (EPS)
Of the myriad facts and figures generated by accountants, the single accounting number that is reported most frequently in the media and receives by far the most attention by investors and creditors is earnings per share.

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Faster Pricing of Convertible Bonds Jean-Noël Dordain, Nabil Kahale and Arnaud Vinciguerra,Senior members of the research team at trading and risk management system specialist Sophis,discuss their latest pricing model for ConvertiblesWe study the pricing of convertible bonds using one-factormethods. Classical numerical algorithms based on latticetrees converge slowly as the number of time-steps increaseswhen there is an issuer call. We describe an improvedalgorithm that has a much better rate of convergence. Ouralgorithm also evaluates accurately other options having atrigger level,such as barrier options. The algorithm is robustand yields smooth prices and Greek parameters as the spotapproaches the trigger level. It is simple to implement and hasessentially the same running time as a lattice tree algorithm.The classical algorithmWe first describe the classical way to price convertible bondswith lattice trees. For simplicity we use binomial treesthroughout the paper,but the extension to trinomial trees ispossible. We also assume that the tree has been constructed sothat up and down movements occur both with probability 0.5.Consider a convertible bond with an issuer call that payscoupons at predetermined dates. At a given node i,j,let bethe continuation value computed from the discounted averagevalue of its two children,taking into account coupons ifthere are any between time-steps i and i+1. The value at nodei,j if the bearer has no right to convert at time-step i is equalto . If the bearer has the right to convert at time-step i andthe issuer call is not valid at the node,the value at node i,j ismax (CV i,j,),where CV i,j is the conversion price. I f theissuer call is valid at the node,the value at node i,j is max(CV i,j,min (R i,)),where R i is the call price.The issuer call is in general valid in certain time periods ifthe spot is above a trigger level. I n such a case,the abovealgorithm has a low rate of convergence,as illustrated in Fig.3. This is because the trigger level of the issuer call does notcoincide with tree levels,and the spacing between tree levelsdecreases slowly compared to the time-step. This point isexplained in detail in the case of barrier options in severalpapers such as [BL94,DKEB95].The improved algorithmThe improved algorithm is in the same spirit as the onedescribed in [DKEB95] to price barrier options. Ouralgorithm uses just one pass,however. For simplicity,we firstdescribe it in the case of an up-and-out barrier option. In theimproved algorithm,we compute the value of the option attime-steps i for decreasing values of i in the usual way. Ateach time-step,however,we check whether there exists anode i,j such that the spot s =s i,j is below the barrier level Hand is above the barrier,where u and d are theup and down movements multiplication factors. I f such anode i,j exists we multiply the option value at node i,j by= (H -s)/(s1- s)if i is the last time-step,and by 2/(1+)otherwise. We observe that such a node i,j does not exist forall time-steps but for roughly half of them. This algorithm canbe easily adapted to double barrier options. I n Fig. 1,wecompare the prices given by the Cox and the Improved Coxalgorithms to a semi-analytic price for a double barrier optiongiven in [S98]. In both algorithms we compute the averageprice corresponding to two successive numbers of iterations.λλλCCCCduss/1=I n Fig. 2,we compare the prices given by the Cox and the Improved Cox algorithms for a down-and-out call as the spot approaches the barrier.Theoretical justificationThe choice of the factor 2/(1+) is motivated by the following. We assume in this argument that the barrier holds throughout the life of the option and there are no discrete dividends,but experimental results show this assumption is unnecessary. Near the barrier,the theoretical value of the option u (s,idt ) at node i,j is approximated by the discounted value of u (s,(i+1)dt ). Moreover,by linear interpolation,It follows that the value of u at node i,j is approximated by the average discounted value of its two children multiplied by 2(H -s ) / (H -s i +1,j +1Note that the multiplication factor tends to 1 as s 1tends to the barrier from above and to 0 as s tends to the barrier from below,ensuring that the price is continuous in terms of the spot. If we used the multiplication factor instead of 2/(1+) the resulting algorithm would still be continuous,but experimental results show it has a lower rate of convergence than our algorithm.λλλλλ).)1(,()1(,(1,11,1dt i s dt i s u j i j i ++++++Fig. 1. Cox and Improved Cox prices in terms of the number of iterations for a double barrier call with initial spot S 0= 100,strike K = 100,volatility = 25%,interest rate r = 10%,dividend rate q = 5%,upper barrier H = 130,lower barrier L = 75,and time to maturity T = 0.25.The semi-analytic price given in [S98] is 4.3806. The Improved Cox price for 3200 iterations is 4.3807.σFig. 2. Cox and Improved Cox prices as the spot approaches the barrier for a down-and-out call with strike K =110,volatility =30%,interest rate r =5%,no dividend rate,barrier L =90,and time to maturity T =1.The number of iterations is fixed at 100.σPricing of ConvertiblesAgain,our algorithm for convertibles pricing is a modification of the classical algorithm,and proceeds by computing the value of the option at time-steps i for decreasing values of i in the usual way. Using the same notation as before,we check at each time-step whether there exists a node i,j such that the spot s =s i,j is below the trigger level H and s 1is above the trigger level. If such a node i,j exists we let C 1be the value of the option at node i,j computed by backward induction in the usual way,and C 2the value of the option if the issuer call were active at node i,j . The final value we assign to node i,j is C=C 1+(1–)C 2,where =if i is the last time-step and= 2/(1+) otherwise.In Fig. 3,we compare the prices given by the Cox and the Improved Cox algorithms for a convertible bond in terms of the number of iterations.λλαλαααFig. 3. Cox and Improved Cox prices in terms of the number of iterations for a convertible bond with initial spot S 0= 550,nominal value N = 500,volatility = 45%,interest rate r = 10%,yearly discrete dividend d = 10,yearly coupon C = 6%,issuer call trigger level H = 580,issuer call redemption value R = 500,issuer call valid on the entire convertible bond lifetime and time to maturity T = 6. The number of iterations ranges from 100 to 2000.σ3. The number of iterations is fixed at 500. The spot price ranges from 380 to 580.In Fig. 4,we compare the prices given by the Cox and the Improved Cox algorithms for a convertible bond as the spot approaches the trigger levelI n Fig. 5,we compare the deltas given by the Cox and the Improved Cox algorithms for a convertible bond as the spot approaches the barrier.SummaryOur algorithm for pricing convertible bonds with an issuer call converges much faster than the usual tree algorithms with almost no additional cost in running time. For a given number of iterations it yields a continuous price as a function of the spot. t also gives accurate and meaningful hedging parameters even as the spot approaches the trigger level. This algorithm is implemented in the Sophis RISQUE software.References[BL94] P. P. Boyle and S. H. Lau,Bumping up against the barrier with the binomial method,The Journal of Derivatives, 1(4) (1994),6-14.[DKEB95] E. Derman,I. Kani,D. Ergener and I. Bardhan, Enhanced numerical methods for options with barriers. Financial Analysts Journal,51(6) (1995),65-74.[S98] J. Sidenius,Double barrier options:valuation by path counting. Journal of Computational Finance,1(3) (1998), 63-79.Fig. 5. Cox and Improved Cox deltas as the spot approaches the issuer call trigger value for the same convertible bond as in Fig.3. The number of iterations is fixed at 500. The spot price ranges from 380 to 580.About SophisSophis specialises in high performance trading and risk management solutions.I n 1989 the company developed its first products,an equities and convertible bonds database integrated with sophisticated analysis tools. Convertibles On-line and Equities On-line are now used by more than 60 organisations worldwide.In 1992 Sophis launched the first version of RISQUE,a straight through trading and risk management system. R SQUE handles the full range of equity and equity derivative instruments - including multi-currency equity baskets,warrants,convertible bonds,exotics and hedging instruments - as well as interest rate and FX cash & derivatives.R SQUE provides decision support,hedging,risk analysis,portfolio and lifecycle management as well as real-time links to electronic trading platforms,global real-time P&L aggregation,historical V AR analysis and a fully integrated back office.With offices in London,New York,Paris,Tokyo and Dublin Sophis supports the trading and risk management operations of many of the world’s leading financial institutions.About the authorsArnaud Vinciguerra - Head of Research &Development at Sophis.Jean-Noël Dordain and Nabil Kahale - Senior members of the Sophis Research Team.For further information contact:London- Andrew Hawa - Tel:+ 44 (0) 20 7680 2700New York- Mark Englehardt - Tel:+ 1 212 625 8900 Paris- Nicolas Roussel - Tel:+ 33 1 44 55 37 73Tokyo- Maroun Tabet - Tel:+ 81 3 54 03 48 30Email:info@Web site:。