You take a short position in 100 European call option contracts, with strike price $50 and maturity three months, on a stock that is trading at $52. The annual volatility of the stock is constant and equal to 22%. The annual, continuous risk-free interest rate is constant and equal to 5%.
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. 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 $53.50 at the end of the first week and $51.125 at the end of the second week. Assume that one week is exactly 1/52 year.