Hull经典衍生品教科书第9版官方PPT,第33章
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期权、期货及其他衍生产品第9版-赫尔】Ch(24)
.
7
CMS swaps
Swap rate observed at time ti is paid at time ti+1 We must
make a convexity adjustment because payments are swap rates (= yield on a par yield bond) Make a timing adjustment because payments are made at time ti+1 not ti
These cannot be accurately valued by assuming that forward rates will be realized
.
6
LIBOR-in Arrears Swap (Equation 33.1,
page 764-765)
Rate is observed at time ti and paid at time ti rather than time ti+1 It is necessary to make a convexity adjustment to each forward rate underlying the waps
Rate is observed in currency Y and applied to a principal in currency X We must make a quanto adjustment to the rate
.
9
Equity Swaps (page 767-768)
.
3
Compounding Swaps (Business Snapshot
Hull经典衍生品教科书第9版官方PPT,第29章
Both the bond price and the strike price should be cash prices not quoted prices
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 5
Forward Bond and Forward Yield
Approximate duration relation between forward bond price, FB, and forward bond yield, yF
FB FB y F D y F or Dy F FB FB yF
where D is the (modified) duration of the forward bond at option maturity
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
Chapter 29 Interest Rate Derivatives: The Standard Market Models
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1ቤተ መጻሕፍቲ ባይዱ
The Complications in Valuing Interest Rate Derivatives (page 673)
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
期权、期货及其他衍生产品第9版-赫尔】Ch(24)
Total return on an equity index is exchanged periodically for a fixed or floating return When the return on an equity index is exchanged for LIBOR the value of the swap is always zero immediately after a payment. This can be used to value the swap at other times.
h
4
Currency Swaps
In theory, a swap where LIBOR in one currency is exchanged for LIBOR in another currency is worth zero
In practice it is sometimes the case that LIBOR in currency A is exchanged for LIBOR plus a spread in currency B
These cannot be accurately valued by assuming that forward rates will be realized
h
6
LIBOR-in Arrears Swap (Equation 33.1,
page 764-765)
Rate is observed at time ti and paid at time ti rather than time ti+1 It is necessary to make a convexity adjustment to each forward rate underlying the swap
h
4
Currency Swaps
In theory, a swap where LIBOR in one currency is exchanged for LIBOR in another currency is worth zero
In practice it is sometimes the case that LIBOR in currency A is exchanged for LIBOR plus a spread in currency B
These cannot be accurately valued by assuming that forward rates will be realized
h
6
LIBOR-in Arrears Swap (Equation 33.1,
page 764-765)
Rate is observed at time ti and paid at time ti rather than time ti+1 It is necessary to make a convexity adjustment to each forward rate underlying the swap
Hull,经典衍生品教科书第9版,官方ppt,第14章
Chapter 14 Wiener Processes and Itô’s Lemma
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1
Stochastic Processes
Describes the way in which a variable such as a stock price, exchange rate or interest rate changes through time Incorporates uncertainties
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
16
ItôProcess (See pages 308)
In an Itô process the drift rate and the variance rate are functions of time dx=a(x,t) dt+b(x,t) dz The discrete time equivalent
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
15
The Example Revisited
A stock price starts at 40 and has a probability distribution of f(40,100) at the end of the year If we assume the stochastic process is Markov with no drift then the process is dS = 10dz If the stock price were expected to grow by $8 on average during the year, so that the year-end distribution is f(48,100), the process would be dS = 8dt + 10dz
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1
Stochastic Processes
Describes the way in which a variable such as a stock price, exchange rate or interest rate changes through time Incorporates uncertainties
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
16
ItôProcess (See pages 308)
In an Itô process the drift rate and the variance rate are functions of time dx=a(x,t) dt+b(x,t) dz The discrete time equivalent
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
15
The Example Revisited
A stock price starts at 40 and has a probability distribution of f(40,100) at the end of the year If we assume the stochastic process is Markov with no drift then the process is dS = 10dz If the stock price were expected to grow by $8 on average during the year, so that the year-end distribution is f(48,100), the process would be dS = 8dt + 10dz
赫尔《期权、期货及其他衍生产品》（第9版）笔记和课后习题详解答案
赫尔《期权、期货及其他衍生产品》（第9版）笔记和课后习题详解答案赫尔《期权、期货及其他衍生产品》（第9版）笔记和课后习题详解完整版>精研学习?>无偿试用20％资料全国547所院校视频及题库全收集考研全套>视频资料>课后答案>往年真题>职称考试第1章引言1.1复习笔记1.2课后习题详解第2章期货市场的运作机制2.1复习笔记2.2课后习题详解第3章利用期货的对冲策略3.1复习笔记3.2课后习题详解第4章利率4.1复习笔记4.2课后习题详解第5章如何确定远期和期货价格5.1复习笔记5.2课后习题详解第6章利率期货6.1复习笔记6.2课后习题详解第7章互换7.1复习笔记7.2课后习题详解第8章证券化与2007年信用危机8.1复习笔记第9章OIS贴现、信用以及资金费用9.1复习笔记9.2课后习题详解第10章期权市场机制10.1复习笔记10.2课后习题详解第11章股票期权的性质11.1复习笔记11.2课后习题详解第12章期权交易策略12.1复习笔记12.2课后习题详解第13章二叉树13.1复习笔记13.2课后习题详解第14章维纳过程和伊藤引理14.1复习笔记14.2课后习题详解第15章布莱克-斯科尔斯-默顿模型15.1复习笔记15.2课后习题详解第16章雇员股票期权16.1复习笔记16.2课后习题详解第17章股指期权与货币期权17.1复习笔记17.2课后习题详解第18章期货期权18.1复习笔记18.2课后习题详解第19章希腊值19.1复习笔记第20章波动率微笑20.1复习笔记20.2课后习题详解第21章基本数值方法21.1复习笔记21.2课后习题详解第22章风险价值度22.1复习笔记22.2课后习题详解第23章估计波动率和相关系数23.1复习笔记23.2课后习题详解第24章信用风险24.1复习笔记24.2课后习题详解第25章信用衍生产品25.1复习笔记25.2课后习题详解第26章特种期权26.1复习笔记26.2课后习题详解第27章再谈模型和数值算法27.1复习笔记27.2课后习题详解第28章鞅与测度28.1复习笔记28.2课后习题详解第29章利率衍生产品：标准市场模型29.1复习笔记29.2课后习题详解第30章曲率、时间与Quanto调整30.1复习笔记30.2课后习题详解第31章利率衍生产品：短期利率模型31.1复习笔记31.2课后习题详解第32章HJM，LMM模型以及多种零息曲线32.1复习笔记32.2课后习题详解第33章再谈互换33.1复习笔记33.2课后习题详解第34章能源与商品衍生产品34.1复习笔记34.2课后习题详解第35章章实物期权35.1复习笔记35.2课后习题详解第36章重大金融损失与借鉴36.1复习笔记36.2课后习题详解。
Hull经典衍生品教科书第官方, ppt课件
Chapter 6 Interest Rate Futures
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
1
Day Count Convention
• Defines:
• the period of time to which the interest rate applies
• day count is Actual/Actual in period? • day count is 30/360?
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
6
Treቤተ መጻሕፍቲ ባይዱsury Bill Prices in the US
John C. Hull 2014
2
Day Count Conventions in the U.S. (Page 132)
Treasury Bonds: Actual/Actual (in period)
Corporate Bonds: 30/360
Money Market Instruments:
John C. Hull 2014
4
Examples continued
• T-Bill: 8% Actual/360:
• 8% is earned in 360 days. Accrual calculated by dividing the actual number of days in the period by 360. How much interest is earned between March 1 and April 1?
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
1
Day Count Convention
• Defines:
• the period of time to which the interest rate applies
• day count is Actual/Actual in period? • day count is 30/360?
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
6
Treቤተ መጻሕፍቲ ባይዱsury Bill Prices in the US
John C. Hull 2014
2
Day Count Conventions in the U.S. (Page 132)
Treasury Bonds: Actual/Actual (in period)
Corporate Bonds: 30/360
Money Market Instruments:
John C. Hull 2014
4
Examples continued
• T-Bill: 8% Actual/360:
• 8% is earned in 360 days. Accrual calculated by dividing the actual number of days in the period by 360. How much interest is earned between March 1 and April 1?
Hull经典衍生品教科书第9版官方PPT,第30章
Chapter 30 Convexity, Timing, and Timing, and Quanto Adjustments
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1
Forward Yields and Forward Prices
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
2
Relationship Between Bond Yields and Prices (Figure 30.1, page 694)
We define the forward yield on a bond as the yield calculated from the forward bond price There is a non-linear relation between bond yields and bond prices It follows that when the forward bond price equals the expected future bond price, the forward yield does not necessarily equal the expected future yield
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
7
Timing Adjustments (Equation 30.4, page
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1
Forward Yields and Forward Prices
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
2
Relationship Between Bond Yields and Prices (Figure 30.1, page 694)
We define the forward yield on a bond as the yield calculated from the forward bond price There is a non-linear relation between bond yields and bond prices It follows that when the forward bond price equals the expected future bond price, the forward yield does not necessarily equal the expected future yield
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
7
Timing Adjustments (Equation 30.4, page
Hull经典衍生品教科书第9版官方PPT,第3章
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 14
Example
S&P 500 futures price is 1,000 Value of Portfolio is $5 million Beta of portfolio is 1.5 What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
4
Basis Risk
Basis is usually defined as the spot price minus the futures price Basis risk arises because of the uncertainty about the basis when the hedge is closed out
Optimal hedge ratio is
ˆS s ˆ ˆ hr ˆF s
where varis ˆF s
Correlation between percentage daily changes for spot and futures
Optimal number of contracts if adjustment for daily settlement
h *Q A QF
ˆ hV A VF
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
Example
S&P 500 futures price is 1,000 Value of Portfolio is $5 million Beta of portfolio is 1.5 What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
4
Basis Risk
Basis is usually defined as the spot price minus the futures price Basis risk arises because of the uncertainty about the basis when the hedge is closed out
Optimal hedge ratio is
ˆS s ˆ ˆ hr ˆF s
where varis ˆF s
Correlation between percentage daily changes for spot and futures
Optimal number of contracts if adjustment for daily settlement
h *Q A QF
ˆ hV A VF
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
Hull,经典衍生品教科书第9版,官方ppt,第11章
T = 0.25 K =30
r = 10% D=0
What are the arbitrage possibilities when p = 2.25 ? p=1?
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 12
7
Lower Bound for European Put Prices; No Dividends
(Equation 11.5, page 241)
p max(Ke -rT–S0, 0)
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
r
D
+
−
−
+
+
−
−
+
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
3
American vs European Options
An American option is worth at least as much as the corresponding European option Cc Pp
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
2
Effect of Variables on Option Pricing (Table 11.1, page 235)
期权期货及其衍生产品,约翰赫尔官方课件
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2012
14
Final Tree; Fig 33.2
E 44.35
J 45.68
B 30.49
F 31.37
K 32.30
A 20.00
C 21.56
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2012
2
Metals
Gold, silver, platinum, palladium, copper, tin, lead, zinc, nickel, aluminium, etc No seasonality; weather unimportant Investment vs consumption metals Some mean reversion (It can become uneconomic to extract a metal) Recycling
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2012
9
Electricity Derivatives continued
A typical contract allows one side to receive a specified number of megawatt hours for a specified price at a specified location during a particular month Types of contracts:
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Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
9
Equity Swaps (page 767-768)
Total return on an equity index is exchanged periodically for a fixed or floating return When the return on an equity index is exchanged for LIBOR the value of the swap is always zero immediately after a payment. This can be used to value the swap at other times.
CMS swaps
Swap rate observed at time ti is pபைடு நூலகம்id at time ti+1 We must
make a convexity adjustment because payments are swap rates (= yield on a par yield bond) Make a timing adjustment because payments are made at time ti+1 not ti
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
2
Variations on Vanilla Interest Rate Swaps
Principal different on two sides Payment frequency different on two sides Can be floating-for-floating instead of floating-forfixed It is still correct to assume that forward rates are realized How should a swap exchanging the 3-month LIBOR for 3-month CP rate be valued?
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
12
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
10
Swaps with Embedded Options
(page 769-771)
Accrual swaps Cancelable swaps Cancelable compounding swaps
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 4
Currency Swaps
In theory, a swap where LIBOR in one currency is exchanged for LIBOR in another currency is worth zero In practice it is sometimes the case that LIBOR in currency A is exchanged for LIBOR plus a spread in currency B This necessitates a small adjustment to the “assume forward LIBOR rate are realized” rule
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
3
Compounding Swaps (Business Snapshot
33.2, page 762-763)
Interest is compounded instead of being paid Example: the fixed side is 6% compounded forward at 6.3% while the floating side is LIBOR plus 20 bps compounded forward at LIBOR plus 10 bps. This type of compounding swap can be valued (approximately) using the “assume forward rates are realized” rule. Approximation is exact if spread over LIBOR for compounding is zero
Fi 2si2 (ti 1 ti )ti 1 Fi i
when valuing a LIBOR-in-arrears swap
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 7
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 5
More Complex Swaps
LIBOR-in-arrears swaps CMS and CMT swaps Differential swaps
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
11
Other Swaps (page 771-772)
Indexed principal swap Commodity swap Volatility swap Bizarre deals (for example, the P&G 5/30 swap in Business Snapshot 33.4 on page 772)
These cannot be accurately valued by assuming that forward rates will be realized
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
6
LIBOR-in Arrears Swap (Equation 33.1,
page 764-765)
Rate is observed at time ti and paid at time ti rather than time ti+1 It is necessary to make a convexity adjustment to each forward rate underlying the swap Suppose that Fi is the forward rate between time ti and ti+1 and si is its volatility We should increase Fi by
Chapter 33 Swaps Revisited
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1
Valuation of Swaps
The standard approach is to assume that forward rates will be realized This works for plain vanilla interest rate and plain vanilla currency swaps, but does not necessarily work for non-standard swaps
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
8
Differential Swaps
Rate is observed in currency Y and applied to a principal in currency X We must make a quanto adjustment to the rate