Question
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,
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.
Quantity | Exercise Price | Option Type (S=Underlying, c= call, p =put) | Price | Delta | Gamma |
200 | S | 120 | 1.0000 | 0.0000 | |
150 | 120 | c | 4.3585 | 0.5362 | 0.0385 |
-120 | 125 | c | 4.1383 | 0.4179 | 0.0268 |
100 | 115 | p | 4.1947 | -0.3289 | 0.0202 |
-100 | 130 | c | 2.5891 | 0.2982 | 0.0238 |
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 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
Exercise price | Option Type | Price | Delta | Gamma |
110 | p | 1.7220 | -0.1994 | 0.0191 |
125 | c | 2.3255 | 0.3505 | 0.0359 |
Based on the above conditions, answer the following questions.
(please use SOLVER in Excel)
1.How many futures contracts should be bought or sold if he uses futures and call option? (+ : Long, -: Short)
2.How many option contracts should be bought or sold if he uses futures and call option? (+ : Long, -: Short)
3.How many futures contracts should be bought or sold if he uses futures and put option? (+ : Long, -: Short)
4.How many option contracts should be bought or sold if he uses futures and put option? (+ : Long, -: Short)
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