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Oil is currently trading at $100. You want to buy oil and store it for 1 year and then sell it at t = 1. Assume the risk free rate is 5% (annual rate with annual compounding). The options below are European with 1 year to maturity.
a) Describe how you can construct a synthetic long oil position (ignore the storage cost) using a Call with K = 90, a Put with K = 90, and the risk free asset.
b) Now assume the 1-year storage cost is $1, payable at t = 0. Suppose the price of a K = 90 Put is $20. What is the highest value of a K = 90 Call such that there is no arbitrage?
c) Suppose the price of the call were $0.10 greater than your answer to part b. Describe how you would construct an arbitrage strategy.
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