You short 200 contracts of a call option on Stock XYZ. The contract multiplier is 100, i. e. each contract is on 100 shares of the stock. Strike price is $50, and the option is currently at the money, i. e. the stock price is $50 right now. Option has 0.08 years to expiration, risk-free interest rate is zero, and volatility of stock returns is 15% per year. a. Using Black Sholes option pricing model, calculate the delta of the call position and determine the number of shares of the underlying stock that you need to buy to hedge the option position initially.
b. Suppose that price of the stock increases to $51. Time to expiration is now 0.07 years. The other parameters are unchanged. Recalculate delta and determine the number of shares you need to buy (sell) to trade to maintain the hedge.