You are given the following data assuming a Black-Scholes model. S = $90 = 28% r=0.04 =0.02 Suppose you sell a 78-strike put with 4 months to expiration.

(i) (3 points) What is the gamma of this put option?

(ii) (3 points) If the underlying were to decrease by $1 over the next short while, what effect would that have on this options delta?

(iii) (2 points) If all of the data above were the same except that the maturity of the put option was 30 years, what is the approximate value of the puts gamma?

(iv) (2 points) You are acting as market maker in this put option. Is there an advantage to delta-gamma hedging versus delta hedging only? How does the process of delta-gamma hedging differ from delta hedging only?