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An underwrite writes 1,000 European calls on a stock. One call option contract is to buy 100 shares of stock. The current stock price is
An underwrite writes 1,000 European calls on a stock. One call option contract is to buy 100 shares of stock. The current stock price is $49, the strike price is $50, the risk-free rate is 5% p.a., the stock price volatility is 20% p.a., the time to maturity is 4 weeks, the expected return from stock is 12% p.a. The Black-Scholes price of the call option is about $2.40 (the value of an option to buy one share is $2.40) and the delta of the call option is 0.522. The stock price and option delta on the last day of the week 1, 2, 3 and 4 evolve as week 1 2 3 4 stock price 46.25 48.13 46.63 48.12 option delta 0.062 0.183 0.007 0.000 The underwriter decides to delta-hedge his positions weekly in the Black-Scholes environment. What is his cumulative cost to sell/buy shares and what is his net gain or loss? [10]
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