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The current S&P 500 index is 2000 and the continuously compounded risk-free interest rate is 2% per year. A market maker received a buy order of 1000 call options on the index with a strike price of 1900 and a maturity of 12 month. The offered price is $210,000. At the same time, he also received a sell order of 1000 put options on the index with the same strike price and maturity at the price of $110,000. Assume that the S&P 500 index pays continuously compounded dividend yield at 2% per year.
1. Should the market maker execute the trade? Why?
2. If your answer to part 1 is yes, describe a hedging strategy to guarantee an arbitrage profit at time zero.
Please show all work.
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