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m o n th s
in 3 months ($)
1,080
1,040 1,000
960 920
570,000
530,000 490,000 450,000 410,000
An option with a strike price of 960 will provide protection against a 10% decline in the portfolio value
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
6
Calculating Relation Between Index Level and Portfolio Value in 3 months
Edition, Copyright © John C. Hull 2019
2
Index Option Example
Consider a call option on an index with a strike price of 900 Suppose 1 contract is exercised when the index level is 880 What is the payoff?
ƒd
f=e-rT[pfu+(1-p)fd ]
Contracts are on 100 times index; they are settled in cash; OEX is American; the XEO and all other are European
Options, Futures, and Other Derivatives, 7th International
10
Range Forward Contract continued
Figure 15.1, page 320
Payoff
Payoff
Asset Price
K1
K2
K1
K2
Asset Price
Short Position
Long Position
Options, Futures, and Other Derivatives, 7th International
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
9
Range Forward Contracts
Have the effect of ensuring that the exchange rate paid or received will lie within a certain range
If index rises to 1040, it provides a 40/1000 or 4% return in 3 months Total return (incl. dividends)=5% Excess return over risk-free rate=2% Excess return for portfolio=4% Increase in Portfolio Value=4+3-1=6% Portfolio value=$530,000
1. The stock starts at price S0 and provides a dividend yield = q
2. The stock starts at price S0e–q T and provides no income
Options, Futures, and Other Derivatives, 7th International
d2
ln( S0
/
K)
(r
q T
2
/ 2)T
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
15
The Binomial Model
S0uS0ƒuFra bibliotekƒ S0d
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
7
Determining the Strike Price (Table 15.2,
page 319)
Value of Index in 3 Expected Portfolio Value
The most popular underlying indices in the U.S. are The S&P 100 Index (OEX and XEO) The S&P 500 Index (SPX) The Dow Jones Index times 0.01 (DJX) The Nasdaq 100 Index
Edition, Copyright © John C. Hull 2019
12
European Options on Stocks Providing Dividend Yield
continued
We can value European options by reducing the stock price to S0e–q T and then behaving as though there is no dividend
4
Example 1
Portfolio has a beta of 1.0 It is currently worth $500,000 The index currently stands at 1000 What trade is necessary to provide insurance against the portfolio value falling below $450,000?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
13
Extension of Chapter 9 Results
(Equations 15.1 to 15.3)
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
3
Using Index Options for Portfolio
Insurance
Suppose the value of the index is S0 and the strike price is K
If a portfolio has a b of 1.0, the portfolio insurance is obtained by buying 1 put option contract on the index for each 100S0 dollars held
If the b is not 1.0, the portfolio manager buys b put options for each 100S0 dollars held
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
5
Example 2
Portfolio has a beta of 2.0 It is currently worth $500,000 and index stands at 1000 The risk-free rate is 12% per annum The dividend yield on both the portfolio and the index is 4% How many put option contracts should be purchased for portfolio insurance?
In both cases, K is chosen to give the appropriate insurance level
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
Options on Stock Indices and Currencies
Chapter 15
Options, Futures, and Other Derivatives, 7th International Edition,
Copyright © John C. Hull 2019
1
Index Options (page 317-327)
Normally the price of the put equals the price of the call
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
Edition, Copyright © John C. Hull 2019
