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Silicon MicroSystems, Inc. (SMSI) stock is currently selling for $100 and the firm pays no dividends. The stocks volatility is 0.30 and the risk-free rate is 8%. Consider the following 6-month call and put options on SMSI stock (assume that contract size is 1 share): 6. Call 1 Call 2 Call 3 Strike $90 Price $12.817 $6.999 $3.380 Delta Gamma $100$110 0.7690.548 0.333 ma 0.0180.024 0.022 Put 1 90 Put 2 Put 3 110 100 Strike Price $2.485$6.403$12.524 Delta 0.2320.3420.667 Gamma 0.018 0.024 0.022 (a) Suppose you own 1,000 shares of SMSI stock and wish to hedge by making your position delta neutral. What option position would make your portfolio delta-neutral if you use the $90 calls? (b) What option position would make your portfolio delta-neutral if you use the $90 puts? (c) Calculate the gamma of your delta-neutral portfolios in parts (a) and (b). Which hedge, the call or put hedge, is more stable? How would you make your put hedge in part (c) both gamma and delta neutral using the $100 strike call options? (d)Suppose in the previous question you believe that SMSIs stock price is not going to move much over the next 6 months and decide to speculate on this stability by entering into a long butterfly spread using the $90, $100, and $110 strike call options in the previous question. Assume the contract size of each option is 1 one share. Carry out the butterfly spread using 1,000 shares. That is, the spread will be constructed by going long 1,000 $90 strike calls, 1,000 $110 strike calls and shorting 2,000 $100 calls. 7. (a) What is the delta of this strategy? (b) What is the gamma of this strategy? (c) How would you make this both delta and gamma neutral (for the option, please use the $90 put option in the previous question)please just do question 7. thank you

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