期货期权及其衍生品配套课件Ch29
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期货期权及其衍生品配套(全34章)Ch01PPT课件
详细描述
期货交易是一种衍生品交易，其基础资产可以是商品、外汇或股票等。交易双方 通过签订期货合约的方式，约定在未来某一特定时间和价格上交割指定数量的基 础资产。期货交易的主要目的是为了规避风险或进行套期保值。
期货交易规则与流程
总结词
期货交易具有严格的交易规则和流程， 包括保证金制度、逐日盯市、交割制度 等。
卖出看跌期权策略
当预期标的资产价格下跌时，卖出看 跌期权获得赚取收益的权利，但获得 权利金。
组合策略
跨式期权组合策略
同时买入相同行权价格的看涨和看跌 期权，以获得赚取收益的权利，但需 支付权利金。
宽跨式期权组合策略
同时买入不同行权价格的看涨和看跌 期权，以获得赚取收益的权利，但需 支付权利金。
06
04
Theta
衡量期权价格对Rho
衡量期权价格对无风险利率的敏感度。
风险度量与控制
风险度量
通过计算期权价格的敏感性指标，如Delta、 Gamma、Theta、Vega和Rho等，来评估 期权的风险敞口。
风险控制
通过设置止损点、动态调整持仓结构、使用 对冲策略等方式，降低或消除期权交易的风 险敞口。
期权风险管理
希腊字母及其应用
希腊字母
包括Delta、Gamma、Theta、Vega和Rho等， 用于描述期权价格变动与标的资产价格、波动
率、剩余到期时间等变量的敏感性。
01
Gamma
衡量Delta对标的资产价格的敏感度。
03
Vega
衡量期权价格对波动率的敏感度。
05
02
Delta
衡量标的资产价格变动对期权价格的影响程 度。
期货期权及其衍生品配套(全34章 )ch01ppt课件
期货交易是一种衍生品交易，其基础资产可以是商品、外汇或股票等。交易双方 通过签订期货合约的方式，约定在未来某一特定时间和价格上交割指定数量的基 础资产。期货交易的主要目的是为了规避风险或进行套期保值。
期货交易规则与流程
总结词
期货交易具有严格的交易规则和流程， 包括保证金制度、逐日盯市、交割制度 等。
卖出看跌期权策略
当预期标的资产价格下跌时，卖出看 跌期权获得赚取收益的权利，但获得 权利金。
组合策略
跨式期权组合策略
同时买入相同行权价格的看涨和看跌 期权，以获得赚取收益的权利，但需 支付权利金。
宽跨式期权组合策略
同时买入不同行权价格的看涨和看跌 期权，以获得赚取收益的权利，但需 支付权利金。
06
04
Theta
衡量期权价格对Rho
衡量期权价格对无风险利率的敏感度。
风险度量与控制
风险度量
通过计算期权价格的敏感性指标，如Delta、 Gamma、Theta、Vega和Rho等，来评估 期权的风险敞口。
风险控制
通过设置止损点、动态调整持仓结构、使用 对冲策略等方式，降低或消除期权交易的风 险敞口。
期权风险管理
希腊字母及其应用
希腊字母
包括Delta、Gamma、Theta、Vega和Rho等， 用于描述期权价格变动与标的资产价格、波动
率、剩余到期时间等变量的敏感性。
01
Gamma
衡量Delta对标的资产价格的敏感度。
03
Vega
衡量期权价格对波动率的敏感度。
05
02
Delta
衡量标的资产价格变动对期权价格的影响程 度。
期货期权及其衍生品配套(全34章 )ch01ppt课件
期货期权及其衍生品配套课件(全34章)Ch09.ppt
Both are worth max(ST , K ) at the maturity of the options They must therefore be worth the same today. This means that
c + Ke -rT = p + S0
Options, Futures, and Other Derivatives, 7th International
C : American Call option price
P : American Put option price
ST :Stock price at option maturity
D : Present value of dividends during option’s life
r : Risk-free rate for maturity T with cont comp
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
7
Lower Bound for European Put Prices; No Dividends
(Equation 9.2, page 208)
p= 1 ?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
10
Early Exercise
4
Calls: An Arbitrage Opportunity?
c + Ke -rT = p + S0
Options, Futures, and Other Derivatives, 7th International
C : American Call option price
P : American Put option price
ST :Stock price at option maturity
D : Present value of dividends during option’s life
r : Risk-free rate for maturity T with cont comp
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
7
Lower Bound for European Put Prices; No Dividends
(Equation 9.2, page 208)
p= 1 ?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
10
Early Exercise
4
Calls: An Arbitrage Opportunity?
期货期权及其衍生品配套课件(全34章)Ch29
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
The value of the derivative is 1200×1.00535/(1.086) or 760.26
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
(Eqn 29.1, p. 660)
Suppose a derivative provides a payoff at time T
dependent on a bond yield, yT observed at time T. Define:
G(yT) : price of the bond as a function of its yield y0 : forward bond yield at time zero sy : forward yield volatility The expected bond price in a world that is FRN wrt P(0,T) is the forward bond price
Edition, Copyright © John C. Hull 2008
4
Convexity Adjustment for Swap
Rate
The expected value of the swap rate for the period T
期权、期货及其他衍生产品第9版-赫尔】Ch
2021/6/19
Copyright © John C. Hull 2014
6
Yield Vols vs Price Vols (Equation 29.4,
page 677)
This relationship implies the following approximation
B D0yy
where y is the forward yield volatility, B is the forward price volatility, and y0 is today’s forward yield Often y is quoted with the understanding that this relationship will be used to calculate B
F F B B D yFo rF F B B DF y y y F F
where D is the (modified) duration of the forward bond at option maturity
Options, Futures, and Other Derivatives, 9th Edition,
Chapter 29 Interest Rate Derivatives: The Standard Market Models
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John
2021/6/19
C. Hull 2014
1
The Complications in Valuing Interest Rate Derivatives (page 673)
期货期权及其衍生品配套课件(全34章)Ch30.ppt
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
2
The Zero Curve
The process for the instantaneous short rate, r, in the traditional risk-neutral world defines the process for the whole zero curve in this world
Short
r
Rate
r
r
r
Time
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
4
Mean Reversion (Figure 30.1, page 675)
Interest rate HIGH interest rate has negative trend
Interest Rate Derivatives: Model of the Short Rate
Chapter 30
Options, Futures, and Other Derivatives, 7th International Edition,
Copyright © John C. Hull 2008
期货期权及其衍生品配套课件(全34章)Ch23.ppt
Options, Futures, and Other Derivatives 7th International
Edition, Copyright © John C. Hull 2008
6
Valuation Example (page 520-522)
Conditional on no earlier default a reference entity has a (risk-neutral) probability of default of 2% in each of the next 5 years. (This is a default intensity)
In the event of default there is a final accrual payment by the buyer
Settlement can be specified as delivery of the bonds or in cash
Suppose payments are made quarterly in the example just considered. What are the cash flows if there is a default after 3 years and 1 month and recovery rate is 40%?
Options, Futures, and Other Derivatives 7th International
Edition, Copyright © John C. Hull 2008
3
Other Details
Payments are usually made quarterly in arrears
期货期权和其他衍生品英文课件 (29)
The mezzanine tranche is repackaged with other mezzanine tranches
ABS CDOs
Senior Tranche (65%) AAA
Mezzanine Tranche (15%) BBB
Mezzanine Tranche (25%) BBB Equity Tranche (5%) Not Rated Equity Tranche (10%)
SPV
The Waterfall
Asset Cash Flows
Senior Tranche Mezzanine Tranche Equity Tranche
ABS CDOs or Mezz CDOs (Simplified)
ABSs
Assets Senior Tranche (80%) AAA
The Aftermath…
A huge amount of new regulation (Basel II.5, Basel III, Dodd-Frank, etc). For example:
Banks required to hold more equity capital with the definition of equity capital being tightened Banks required to satisfy liquidity ratios CCPs and SEFs for OTC derivatives Bonuses limited in Europe Bonuses spread over several years Proprietary trading restricted
Securitization and the Credit Crisis of 2007
期权期货及其衍生产品约翰赫尔官方课件
Bond: 8% Actual/ Actual in period.
4% is earned between coupon payment dates. Accruals on an Actual basis. When coupons are paid on March 1 and Sept 1, how much interest is earned between March 1 and April 1?
Chapter 6 Interest Rate Futures
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2019
1
Day Count Convention
Defines:
the period of time to which the interest rate applies The period of time used to calculate accrued interest (relevant when the instrument is bought of sold
P 360 (100 Y ) n
Y is cash price per $100 P is quoted price
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2019
7
Treasury Bond Price Quotes in the U.S
Cash price received by party with short position = Most recent settlement price × Conversion factor + Accrued interest
4% is earned between coupon payment dates. Accruals on an Actual basis. When coupons are paid on March 1 and Sept 1, how much interest is earned between March 1 and April 1?
Chapter 6 Interest Rate Futures
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2019
1
Day Count Convention
Defines:
the period of time to which the interest rate applies The period of time used to calculate accrued interest (relevant when the instrument is bought of sold
P 360 (100 Y ) n
Y is cash price per $100 P is quoted price
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2019
7
Treasury Bond Price Quotes in the U.S
Cash price received by party with short position = Most recent settlement price × Conversion factor + Accrued interest
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exprVR sV 1s RR R00/(Tm*T)T
where R is the forward interest rate between T and T* expressed with a compounding frequency of m, sR is the volatility of R, R0 is the value of R today, sV is the volatility of F, and r is the correlation between R and V
multiplied by exp(rVWsVsWT)
W is the forward exchange rate (units of Y per unit of X) and rVW is the correlation between V and W.
Options, Futures, and Other Derivatives, 7th International
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
2
Relationship Between Bond Yields and Prices (Figure 29.1, page 660)
The expected bond yield in a world that is FRN wrt
P(0,T)F is orB w oa Y nr id 1 2 d e y0 2 s l2 y d TG G ( (y y 0 0 ) )
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
Байду номын сангаас12
Example 29.4 (page 666)
Current value of Nikkei index is 15,000
This gives one-year forward as 15,150.75
Suppose the volatility of the Nikkei is 20%, the volatility of the dollar-yen exchange rate is 12% and the correlation between the two is 0.3
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
7
Timing Adjustments (Equation 29.4,
page 664)
The expected value of a variable, V, in a world that is FRN wrt P(0,T*) is the expected value of the variable in a world that is FRN wrt P(0,T) multiplied by
(Eqn 29.1, p. 660)
Suppose a derivative provides a payoff at time T
dependent on a bond yield, yT observed at time T. Define:
G(yT) : price of the bond as a function of its yield y0 : forward bond yield at time zero sy : forward yield volatility The expected bond price in a world that is FRN wrt P(0,T) is the forward bond price
9
Quantos
(Section 29.3, page 665)
Quantos are derivatives where the payoff is defined using variables measured in one currency and paid in another currency Example: contract providing a payoff of ST – K dollars ($) where S is the Nikkei stock index (a yen number)
The one-year forward value of the Nikkei for a contract settled in dollars is 15,150.75e0.3 ×0.2×0.12×1 or 15,260.23
Options, Futures, and Other Derivatives, 7th International
Quanto, Timing, and Convexity Adjustments
Chapter 29
Options, Futures, and Other Derivatives, 7th International Edition,
Copyright © John C. Hull 2019
1
Forward Yields and Forward Prices
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
10
Diff Swap
Diff swaps are a type of quanto A floating rate is observed in one currency and applied to a principal in another currency
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, 7th International
Edition, Copyright © John C. Hull 2019
8
Example 29.3 (page 664)
A derivative provides a payoff 6 years equal to the value of a stock index in 5 years. The interest rate is 8% with annual compounding
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
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
5
Example 29.1 (page 662)
An instrument provides a payoff in 3 years equal to the 1-year zero-coupon rate multiplied by $1000
1200 is the 5-year forward value of the stock index
This is the expected value in a world that is FRN wrt P(0,5)
To get the value in a world that is FRN wrt P(0,6) we multiply by 1.00535
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
11
Quanto Adjustment (page 666)
The expected value of a variable, V, in a world that is FRN wrt PX(0,T) is its expected value in a world that is FRN wrt PY(0,T)
Volatility is 20%
Yield curve is flat at 10% (with annual compounding)
The convexity adjustment is 10.9 bps so that
the value of the instrument is 101.09/1.13 =
ForS w w R aa r ad p 1 2ty0 2 e s 2 yTG G ((y y0 0))
where G(y) defines the relationship between price and yield for a bond lasting between T and T+t that pays a coupon equal to the forward swap rate
where R is the forward interest rate between T and T* expressed with a compounding frequency of m, sR is the volatility of R, R0 is the value of R today, sV is the volatility of F, and r is the correlation between R and V
multiplied by exp(rVWsVsWT)
W is the forward exchange rate (units of Y per unit of X) and rVW is the correlation between V and W.
Options, Futures, and Other Derivatives, 7th International
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
2
Relationship Between Bond Yields and Prices (Figure 29.1, page 660)
The expected bond yield in a world that is FRN wrt
P(0,T)F is orB w oa Y nr id 1 2 d e y0 2 s l2 y d TG G ( (y y 0 0 ) )
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
Байду номын сангаас12
Example 29.4 (page 666)
Current value of Nikkei index is 15,000
This gives one-year forward as 15,150.75
Suppose the volatility of the Nikkei is 20%, the volatility of the dollar-yen exchange rate is 12% and the correlation between the two is 0.3
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
7
Timing Adjustments (Equation 29.4,
page 664)
The expected value of a variable, V, in a world that is FRN wrt P(0,T*) is the expected value of the variable in a world that is FRN wrt P(0,T) multiplied by
(Eqn 29.1, p. 660)
Suppose a derivative provides a payoff at time T
dependent on a bond yield, yT observed at time T. Define:
G(yT) : price of the bond as a function of its yield y0 : forward bond yield at time zero sy : forward yield volatility The expected bond price in a world that is FRN wrt P(0,T) is the forward bond price
9
Quantos
(Section 29.3, page 665)
Quantos are derivatives where the payoff is defined using variables measured in one currency and paid in another currency Example: contract providing a payoff of ST – K dollars ($) where S is the Nikkei stock index (a yen number)
The one-year forward value of the Nikkei for a contract settled in dollars is 15,150.75e0.3 ×0.2×0.12×1 or 15,260.23
Options, Futures, and Other Derivatives, 7th International
Quanto, Timing, and Convexity Adjustments
Chapter 29
Options, Futures, and Other Derivatives, 7th International Edition,
Copyright © John C. Hull 2019
1
Forward Yields and Forward Prices
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
10
Diff Swap
Diff swaps are a type of quanto A floating rate is observed in one currency and applied to a principal in another currency
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, 7th International
Edition, Copyright © John C. Hull 2019
8
Example 29.3 (page 664)
A derivative provides a payoff 6 years equal to the value of a stock index in 5 years. The interest rate is 8% with annual compounding
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
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
5
Example 29.1 (page 662)
An instrument provides a payoff in 3 years equal to the 1-year zero-coupon rate multiplied by $1000
1200 is the 5-year forward value of the stock index
This is the expected value in a world that is FRN wrt P(0,5)
To get the value in a world that is FRN wrt P(0,6) we multiply by 1.00535
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
11
Quanto Adjustment (page 666)
The expected value of a variable, V, in a world that is FRN wrt PX(0,T) is its expected value in a world that is FRN wrt PY(0,T)
Volatility is 20%
Yield curve is flat at 10% (with annual compounding)
The convexity adjustment is 10.9 bps so that
the value of the instrument is 101.09/1.13 =
ForS w w R aa r ad p 1 2ty0 2 e s 2 yTG G ((y y0 0))
where G(y) defines the relationship between price and yield for a bond lasting between T and T+t that pays a coupon equal to the forward swap rate