Ch17 - The Greek Letters Chapter 17 1 Example A bank has...

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The Greek Letters Chapter 17 1
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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 S 0 = 49, K = 50, r = 5%, σ = 20%, T = 20 weeks, μ = 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? 2
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Naked position Take no action Covered position Buy 100,000 shares today Both strategies leave the bank exposed to significant risk 3
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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 4
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Delta (See Figure 17.2, page 353) Delta ( ) is the rate of change of the option price with respect to the underlying 5 Option price A B Slope = Stock price
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Delta Hedging This involves maintaining a delta neutral portfolio The delta of a European call on a non- dividend paying stock is N ( d 1 ) The delta of a European put on the stock is N ( d 1 ) – 1 6
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Delta Hedging continued The hedge position must be frequently
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Ch17 - The Greek Letters Chapter 17 1 Example A bank has...

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