You Purchase a call option with a strike price of $30 and 4 months until expiration on a stock that pays a 2% dividend and has a 22% volatility when the risk-free interest rate is 4%. The spot price of the underlying is $32.
1. What is the price of the option?
2. If your want to hedge the position, how many shares of the underlying stock do you need to buy or sell?
3. Assume that gamma is 0.1. if the stock price gose up to $.50, what is the approximate value of the option, using the delta-gamma approximation?