QUESTION 4 15+ 2 + 3 + 3 = 13 marks) You work for Sheldon & Cooper, a financial intermediary. Currently, the company's options book shows a short position. Specifically, Sheldon & Cooper has written to various clients a total of 15,000 European 3-month put contracts on stocks issued by the Farrah Fowler company. The puts have a strike price of $860 and an implied volatility of 40% p.a., while the stock is currently trading at $850 and offers a dividend yield of 0.5% p.a. The contract size is, as usual, 100 shares. You can assume a riskfree interest rate of 0.50% p.a. compounded continuously, a) Using the BSM model, compute the Delta, Gamma, Rho, Vega and Theta of the overall option position at Sheldon & Cooper. Next, you need to explain to your boss in plain English the meaning of each computed Greek letter. b) Sheldon & Cooper wants its portfolio to be Delta neutral. What trade needs to be made in order to do so? c) Carefully explain the meaning and the risks of the delta neutral position for Sheldon & Cooper. (Use no more than three sentences.) d) Understanding the limitations of delta hedging, your boss wants you to recommend trades that make the company's portfolio gamma neutral as well. In order to add gamma neutrality you are allowed to trade in 2-month calls on the same stock with a strike of 835. The calls have the same implied vol. as the puts the company has written. Detail the trades that need to be made. NOTE: For all answers show your calculations. For underlying asset units and number of options contracts, round to the nearest integer. In part a and d, round d1 and d2 to 2 decimal digits only when you need to compute the normal probabilities from the Normal Table. For all other calculations, including di and d2, round to 4 decimal digits at each step. QUESTION 4 15+ 2 + 3 + 3 = 13 marks) You work for Sheldon & Cooper, a financial intermediary. Currently, the company's options book shows a short position. Specifically, Sheldon & Cooper has written to various clients a total of 15,000 European 3-month put contracts on stocks issued by the Farrah Fowler company. The puts have a strike price of $860 and an implied volatility of 40% p.a., while the stock is currently trading at $850 and offers a dividend yield of 0.5% p.a. The contract size is, as usual, 100 shares. You can assume a riskfree interest rate of 0.50% p.a. compounded continuously, a) Using the BSM model, compute the Delta, Gamma, Rho, Vega and Theta of the overall option position at Sheldon & Cooper. Next, you need to explain to your boss in plain English the meaning of each computed Greek letter. b) Sheldon & Cooper wants its portfolio to be Delta neutral. What trade needs to be made in order to do so? c) Carefully explain the meaning and the risks of the delta neutral position for Sheldon & Cooper. (Use no more than three sentences.) d) Understanding the limitations of delta hedging, your boss wants you to recommend trades that make the company's portfolio gamma neutral as well. In order to add gamma neutrality you are allowed to trade in 2-month calls on the same stock with a strike of 835. The calls have the same implied vol. as the puts the company has written. Detail the trades that need to be made. NOTE: For all answers show your calculations. For underlying asset units and number of options contracts, round to the nearest integer. In part a and d, round d1 and d2 to 2 decimal digits only when you need to compute the normal probabilities from the Normal Table. For all other calculations, including di and d2, round to 4 decimal digits at each step