A stock option market maker has a portfolio consisting of 200 shares of ABC Corp, and the following option positions on ABC Corp. For simplicity, each option is assumed to be written on a single share of the stock.

The market maker is worried about stock price movements in ABCs stock and would like to make his portfolio delta-neutral and gamma neutral over the night. The current stock price of ABC is $120, the volatility of the stock is 30%, and the risk-free rate is 5%. The market maker can form the hedge using a 3-month futures on ABC stock whose price is at full carry and either one of two options on ABC stock whose attributes are

(a) How many futures and option contracts should be bought or sold if he uses futures and call option?

(b) How many futures and option contracts should be bought or sold if he uses futures and put option?

(c) If transaction costs are $ 5 per contracts, which instruments should be selected to achieve delta-neutral and gamma-neutral?

Quantity Exercise Price Option Type Price Delta Gamma 200 150 -120 100 -100 120 125 115 130 120.0000 1.0000 0.0000 4.3585 0.5362 0.0385 4.1383 0.4179 0.0268 4.19470.3289 0.0202 2.58910.2982 0.0238 Exercise Price Option Type Price Delta Gamma 1.7220 -0.1994 0.0191 110 125 2.3255 0.3505 0.0359