文档介绍：The Greek Letters Chapter 14
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Example
A bank has sold for $300,000 a European call option on 100,000 shares of a nondividend paying stock
S0 = 49, K = 50, r = 5%, s = 20%,
T = 20 weeks, m = 13%
The Black-Scholes value of the option is $240,000
How does the bank hedge its risk to lock in a $60,000 profit?
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Naked & Covered Positions
Naked position
Take no action
Covered position
Buy 100,000 shares today
Both strategies leave the bank exposed to significant risk
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Stop-Loss Strategy
This involves:
Buying 100,000 shares as soon as price reaches $50
Selling 100,000 shares as soon as price falls below $50
This deceptively simple hedging strategy does not work well
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Delta (See Figure , page 302)
Delta (D) is the rate of change of the option price with respect to the underlying
Option
price
A
B
Slope = D
Stock price
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Delta Hedging
This involves maintaining a delta neutral portfolio
The delta of a European call on a stock paying dividends at rate q is N (d 1)e– qT
The delta of a European put is
e– qT [N (d 1) – 1]
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Delta Hedging continued
The hedge position must be frequently rebalanced
Delta hedging a written option involves a “buy high, sell low” trading rule
See Tables (page 307) and (page 308) for examples of delta hedging
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Using Futures for Delta Hedging
The delta of a futures contract is e(r-q)T times the delta of a spot contract
The position required in futures for delta hedging is t