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Delta Hedging
This involves maintaining a delta neutral portfolio The delta of a European call on a nondividend paying stock is N (d 1) The delta of a European put on the stock is
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Stop-Loss Strategy continued
Ignoring discounting, the cost of writing and hedging the option appears to be max(S0−K, 0). What are we overlooking?
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Naked & Covered Positions
Naked position
Take no action
Covered position
N (d 1) – 1
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The Costs in Delta Hedging continued
Delta hedging a written option involves a “buy high, sell low” trading rule
Call option price
Slope = D = 0.6 B
A Stock price
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Hedge
Trader would be hedged with the position:
Chapter 18 The Greek Letters
Options, Futures, and Other Derivatives, 8th Edition,
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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?
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
3
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
Options, Futures, and Other Derivatives, 8th Edition,
Buy 100,000 shares today
What are the risks associated with these strategies?
Options, Futures, and Other Derivatives, 8th Edition,
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Options, Futures, and Other Derivatives, 8th Edition,
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5
Delta (See Figure 18.2, page 381)
Delta (D) is the rate of change of the option price with respect to the underlying
.......
2,557.8 2,252.3 1,979.8
.......
2.5 2.2 1.9 .......
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First Scenario for the Example:
Table 18.2 page 384
Байду номын сангаас
Week
Stock price
Delta Shares
Cost
Cumulative
purchased (‘$000) Cost ($000)
Interest
0 1 2 .......
49.00 48.12 47.37 .......
0.522 0.458 0.400 .......
52,200 (6,400) (5,800)
.......
2,557.8 (308.0) (274.7)