You take a short position in 100 European call option contracts with strike price $50 and maturity.
QUESTION
You take a short position in 100 European call option contracts, with strike price $50 and maturity 3 months, on a stock that is trading at $52. The annual volatility of the stock is constant and equal to 22%. The annual risk-free interest rate is constant and equal to 5%, the dividend yield is zero. Suppose that you sold the options at a premium of 10% over the Black-Scholes price. You hedge your portfolio with the underlying stock and the risk-free asset, using the Black-Scholes model. The hedge is rebalanced weekly. After two weeks the portfolio is liquidated. Compute the final profit or loss, if the price of the stock is $54.00 at the end of the first week, and $51.00 at the end of thesecond week. Assume that one week is exactly 1/52 years.Question is attached
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You take a short position in 100 European call option contracts, with strike price $50 and maturity 3 months, on a stock that is trading at $52. The annual volatility of the stock is constant and equal to 22%. The annual risk-free interest rate is constant and equal to 5%, the dividend yield is zero. Suppose that you sold the options at a premium of 10% over the Black-Scholes price. You hedge your portfolio with the underlying stock and the risk-free asset, using the Black-Scholes model. The hedge is rebalanced weekly. After two weeks the portfolio is liquidated. Compute the final profit or loss, if the price of the stock is $54.00 at the end of the first week, and $51.00 at the end of the second week. Assume that one week is exactly 1/52 years.
ANSWER:
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