Delta 2. A stock option market maker has a portfolio consisting of 100 shares of ABC Corp, and the following option positions on ABC Corp. For simplicity, each option is as- sumed to be written on a single share of the stock. Quantity Exercise Price Option Type Price Gamma 100 S 120.0000 1.0000 0.0000 150 4.3585 0.5362 0.0385 -120 4.1383 0.4179 0.0268 100 115 4.1947 -0.3289 0.0202 -100 130 2.5891 0.2982 0.0238 120 125 The market maker is worried about stock price movements in ABC's stock and would like to make his portfolio delta-neutral and gamma neutral over the night. The cur- rent 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 futures on ABC stock whose price is at full carry and either one of two options on ABC stock whose attributes are Exercise Price Option Type Price Delta Gamma 110 P 1.7220 -0.1994 0.0191 125 2.3255 0.3505 0.0359 (a) How many futures and option contracts should be bought or sold if he uses futures and call option? (6) 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? Delta 2. A stock option market maker has a portfolio consisting of 100 shares of ABC Corp, and the following option positions on ABC Corp. For simplicity, each option is as- sumed to be written on a single share of the stock. Quantity Exercise Price Option Type Price Gamma 100 S 120.0000 1.0000 0.0000 150 4.3585 0.5362 0.0385 -120 4.1383 0.4179 0.0268 100 115 4.1947 -0.3289 0.0202 -100 130 2.5891 0.2982 0.0238 120 125 The market maker is worried about stock price movements in ABC's stock and would like to make his portfolio delta-neutral and gamma neutral over the night. The cur- rent 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 futures on ABC stock whose price is at full carry and either one of two options on ABC stock whose attributes are Exercise Price Option Type Price Delta Gamma 110 P 1.7220 -0.1994 0.0191 125 2.3255 0.3505 0.0359 (a) How many futures and option contracts should be bought or sold if he uses futures and call option? (6) 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
