You are a market maker for options on a stock index. You have just written 100...

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You are a market maker for options on a stock index. You have just written 100 European put options on the stock index with a strike price of KPut = 35 that expires in 360 days. You have decided to delta-gamma hedge your position with weekly rebalancing. The current price of the stock index is S = 40. • The volatility of the stock index is o = 0.32. • The continuously compounded interest rate is r = 0.04 per period. • The continuous dividend yield rate is 6 = 0 per period. • You have selected a call option on the stock index expiring in 90 days with a strike price of Kcall = 45 to use as your initial source of gamma. • All options transactions occur at the Black-Scholes prices. One year equals 365 days. One week equals 7 days. Your experience with the market over the past two weeks is summarized in the fol- lowing table. Put Option (K = 35) Call Option (K =45) Delta Gamma Price Delta Gamma 2.13652 -0.24096 0.02451 0.99101 0.27435 0.05244 1.67262 -0.19500 0.02086 1.53674 0.37592 0.05921 2.91861 -0.32425 0.03119 0.27924 0.11305 0.03549 Time (Days) Index Price 40 42 37 0 7 14 (a) (4 points) What position did you take in the stock index and call options in order to establish your initial delta-gamma hedge position? (b) (6 points) You delta-gamma hedged for two weeks. What is your P&L at the end of the two weeks? You are a market maker for options on a stock index. You have just written 100 European put options on the stock index with a strike price of KPut = 35 that expires in 360 days. You have decided to delta-gamma hedge your position with weekly rebalancing. The current price of the stock index is S = 40. • The volatility of the stock index is o = 0.32. • The continuously compounded interest rate is r = 0.04 per period. • The continuous dividend yield rate is 6 = 0 per period. • You have selected a call option on the stock index expiring in 90 days with a strike price of Kcall = 45 to use as your initial source of gamma. • All options transactions occur at the Black-Scholes prices. One year equals 365 days. One week equals 7 days. Your experience with the market over the past two weeks is summarized in the fol- lowing table. Put Option (K = 35) Call Option (K =45) Delta Gamma Price Delta Gamma 2.13652 -0.24096 0.02451 0.99101 0.27435 0.05244 1.67262 -0.19500 0.02086 1.53674 0.37592 0.05921 2.91861 -0.32425 0.03119 0.27924 0.11305 0.03549 Time (Days) Index Price 40 42 37 0 7 14 (a) (4 points) What position did you take in the stock index and call options in order to establish your initial delta-gamma hedge position? (b) (6 points) You delta-gamma hedged for two weeks. What is your P&L at the end of the two weeks?

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a To establish the initial deltagamma hedge position we need to determine the number of stock index ... View the full answer