Question 6.1: Suppose that S(0) = 17 dollars, F(0,1) = 18 dollars, r = 8%,...

Suppose that S(0) = 17 dollars, F(0, 1) = 18 dollars, r = 8%, and short selling requires a 30% security deposit attracting interest at d = 4%. Is there an arbitrage opportunity? Find the highest rate d for which there is no arbitrage opportunity.

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Yes, there is an arbitrage opportunity. We enter into a long forward contract and sell short one share, investing 70% of the proceeds at 8% and paying the remaining 30% as a security deposit to attract interest at 4%. At the time of delivery the cash investments plus interest will be worth about $18.20, out of which $18 will need to be paid for one share to close out the short position in stock. This leaves a $0.20 arbitrage profit. The rates d for the security deposit such that there is no arbitrage opportunity satisfy 30\% × 17 × e^{d} + 70\% × 17 × e^{8\% }≤ 18. The highest such rate is d≅0.1740\%.

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