You have the following information on a European call option. The option has a strike price of $80 and 8 months to expiration. The underlying stock is currently trading at $82 pays dividends at a rate of 1.5%, and has historical volatility of 25%. The risk-free rate is 4%.
a. Compute the option’s delta.
b. You purchase 100 options (you will need to calculate the price of the option) and go short the appropriate number of shares to hedge the position (for simplicity, assume that one option controls one share and that you must buy or sell whole shares of stock by rounding at 0.5)Assume that the stock price increases to 85 immediately so that no time has passed. Recalculate the option price using the Black-Scholes equation. Compute the total profit. (There is no need to consider interest on the short proceeds because no time has passed between valuations.)
3. What is the volatility of the call option from problem.