(30 Points) Assume a futures option market maker is short (a) 100 calls with an exercise price of 80, (b) 150 puts with an exercise price of 90, (c) 250 calls with an exercise price of 110, and (d) 200 puts with an exercise price of 120. All options have three-month remaining to expiration. The market maker would like to make his portfolio both delta-neutral and gamma-neutral using 3-month futures and either the 100 call or the 100 put. The current 3-month futures price is 101.2578, the interest rate is 5%, and the volatility rate is 30%. The current option values and their "Greeks" are as follows: Call Option Value Delta Gamma Exercise Put Option PriceV Value DeltaGamma 8021.3248 0.9501 0.00690.3311 -0.0499 0.0069 [t] 0.0184 0.0263 0.0237 120 1.0492 0.1452 0.015219.5585 -0.8548 0.0152 [b] 9012.8582 0.8053 0.0184 1.7402 -0.1947 100 6.5831 0.5629 0.0263 5.3409 -0.4371 110 2.8444 0.3167 0.0237 11.4780 -0.6833 Assume that the market maker wants to minimize transaction costs and the transac- tion cost rate is $5 per contract, how many futures and option contracts should be bought/sold? (30 Points) Assume a futures option market maker is short (a) 100 calls with an exercise price of 80, (b) 150 puts with an exercise price of 90, (c) 250 calls with an exercise price of 110, and (d) 200 puts with an exercise price of 120. All options have three-month remaining to expiration. The market maker would like to make his portfolio both delta-neutral and gamma-neutral using 3-month futures and either the 100 call or the 100 put. The current 3-month futures price is 101.2578, the interest rate is 5%, and the volatility rate is 30%. The current option values and their "Greeks" are as follows: Exercise Call Option Put Option Price Value Delta Gamma ValueDelta Gamma 8021.3248 0.9501 0.00690.3311 -0.0499 0.0069 [t] 0.0184 0.0263 0.0237 120 1.0492 0.1452 0.015219.5585 -0.8548 0.0152 [b] 9012.8582 0.8053 0.0184 1.7402 -0.1947 100 6.5831 0.5629 0.0263 5.3409 -0.4371 110 2.8444 0.3167 0.0237 11.4780 -0.6833