The following information is given about an Option on a stock: S(0)=$31, X=$34, rf=9%, variance (sigma squared)=20%, T=182.5 days, Dividend $1.75 in 45 days

(5) Calculate Gamma for the option (show all workings) (6) If the stock price moves from $31 to $27, what is the expected change in Delta and what is your new share holdings (assuming you hedge) (7) Calculate Vega for the put option (show all workings) (8) If the volatility converges to your estimated volatility figure from the question above (10\% higher than implied volatility) what price is the put option expected to move to