Hull经典衍生品教科书第9版官方第21章精品PPT课件
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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
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
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版官方第19章精品PPT课件
Buy 100,000 shares today
What are the risks associated with these strategies?
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
5
Delta (See Figure 19.2, page 403)
Delta (D) is the rate of change of the option price with respect to the underlying
short 1000 options buy 600 shares
Gain/loss on the option position is offset by loss/gain on stock position Delta changes as stock price changes and time passes Hedge position must therefore be rebalanced
Chapter 19 The Greek Letters
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
1
Example
A bank has sold for $300,000 a European call option on 100,000 shares of a non-dividend paying stock S0 = 49, K = 50, r = 5%, s = 20%, T = 20 weeks, m = 13% The Black-Scholes-Merton value of the option is $240,000 How does the bank hedge its risk to lock in a $60,000 profit?
What are the risks associated with these strategies?
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
5
Delta (See Figure 19.2, page 403)
Delta (D) is the rate of change of the option price with respect to the underlying
short 1000 options buy 600 shares
Gain/loss on the option position is offset by loss/gain on stock position Delta changes as stock price changes and time passes Hedge position must therefore be rebalanced
Chapter 19 The Greek Letters
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
1
Example
A bank has sold for $300,000 a European call option on 100,000 shares of a non-dividend paying stock S0 = 49, K = 50, r = 5%, s = 20%, T = 20 weeks, m = 13% The Black-Scholes-Merton value of the option is $240,000 How does the bank hedge its risk to lock in a $60,000 profit?
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)
Hull经典衍生品教科书第9版官方PPT,第5章
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
2
Short Selling (Page 105-106)
Short selling involves selling securities you do not own Your broker borrows the securities from another client and sells them in the market in the usual way
Is there an arbitrage opportunity?
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
8
The Forward Price
If the spot price of an investment asset is S0 and the futures price for a contract deliverable in T years is F0, then
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
3
Short Selling (continued)
At some stage you must buy the securities so they can be replaced in the account of the client You must pay dividends and other benefits the owner of the securities receives There may be a small fee for borrowing the securities
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a e0.11/12 1.0084 u e0.4 1/12 1.1224 d 1 0.8909
u p 1.0084 0.8909 0.5073
1.1224 0.8909
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
Chapter 21 Basic Numerical Procedures
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
1
Approaches to Derivatives Valuation
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
3
Movements in Time Dt
(Figure 21.1, page 451)
Su
S Sd
Options, Futures, and Other Derivatives, 9th Edition,
d es Dt p ad
ud a e(r q) Dt
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
6
The Complete Tree
(Figure 21.2, page 453)
Copyright © John C. Hull 2014
4
Tree Parameters for asset paying a dividend yield of q
Parameters p, u, and d are chosen so that the tree gives correct values for the mean & variance of the stock price changes in a risk-neutral world
Trees Monte Carlo simulation Finite difference methods
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
2
Binomial Trees
S0u4
S0u2
S0u3
S0u
S0u
S0u2
S0
S0
S0
S0d
S0d
S0d2
S0d3
S0d2
S0d4
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
7
Backwards Induction
50.00 4.49
56.12 2.16
44.55 6.96
62.99 0.64
50.00 3.77
39.69 10.36
Node Time: 0.0000
0.0833
0.1667
70.70 0.00
56.12 1.30
44.55 6.38
35.36 14.64
0.2500
79.35 0.00
Mean: Variance:
e(r−q)Dt = pu + (1– p )d s2Dt = pu2 + (1– p )d 2 – e2(r−q)Dt
A further condition often imposed is u = 1/ d
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
5
Tree Parameters for asset paying a dividend yield of q
(continued)
When Dt is small a solution to the equations is
u es Dt
We know the value of the option at the final nodes We work back through the tree using risk-neutral valuation to calculate the value of the option at each node, testing for early exercise when appropriate
9
Example (continued; Figure 21.3, page 454)
At each node: Upper value = Underlying Asset Price Lower value = Option Price Values in red are a result of exercise.
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
8
Example: Put Option
(Example 21.1, page 453-455)
S0 = 50; K = 50; r =10%; s = 40%; T = 5 months = 0.4167; Dt = 1 month = 0.0833 In this case
Binomial trees are frequently used to approximate the movements in the price of a stock or other asset In each small interval of time the stock price is assumed to move up by a proportional amount u or to move down by a proportional amount d
u p 1.0084 0.8909 0.5073
1.1224 0.8909
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
Chapter 21 Basic Numerical Procedures
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
1
Approaches to Derivatives Valuation
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
3
Movements in Time Dt
(Figure 21.1, page 451)
Su
S Sd
Options, Futures, and Other Derivatives, 9th Edition,
d es Dt p ad
ud a e(r q) Dt
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
6
The Complete Tree
(Figure 21.2, page 453)
Copyright © John C. Hull 2014
4
Tree Parameters for asset paying a dividend yield of q
Parameters p, u, and d are chosen so that the tree gives correct values for the mean & variance of the stock price changes in a risk-neutral world
Trees Monte Carlo simulation Finite difference methods
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
2
Binomial Trees
S0u4
S0u2
S0u3
S0u
S0u
S0u2
S0
S0
S0
S0d
S0d
S0d2
S0d3
S0d2
S0d4
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
7
Backwards Induction
50.00 4.49
56.12 2.16
44.55 6.96
62.99 0.64
50.00 3.77
39.69 10.36
Node Time: 0.0000
0.0833
0.1667
70.70 0.00
56.12 1.30
44.55 6.38
35.36 14.64
0.2500
79.35 0.00
Mean: Variance:
e(r−q)Dt = pu + (1– p )d s2Dt = pu2 + (1– p )d 2 – e2(r−q)Dt
A further condition often imposed is u = 1/ d
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
5
Tree Parameters for asset paying a dividend yield of q
(continued)
When Dt is small a solution to the equations is
u es Dt
We know the value of the option at the final nodes We work back through the tree using risk-neutral valuation to calculate the value of the option at each node, testing for early exercise when appropriate
9
Example (continued; Figure 21.3, page 454)
At each node: Upper value = Underlying Asset Price Lower value = Option Price Values in red are a result of exercise.
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
8
Example: Put Option
(Example 21.1, page 453-455)
S0 = 50; K = 50; r =10%; s = 40%; T = 5 months = 0.4167; Dt = 1 month = 0.0833 In this case
Binomial trees are frequently used to approximate the movements in the price of a stock or other asset In each small interval of time the stock price is assumed to move up by a proportional amount u or to move down by a proportional amount d