Two simple experiments are ip a coin and roll a die

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Unformatted text preview: able to buy any amounts (even negative) of these bets. Is there an arbitrage opportunity? (b) What if only the first two bets are available? 6.5. Suppose Microsoft stock sells for 100 while Netscape sells for 50. Three possible outcomes of a court case will have the following impact on the two stocks. 204 CHAPTER 6. MATHEMATICAL FINANCE 1 (win) 2 (draw) 3 (lose) Microsoft 120 110 84 Netscape 30 55 60 What should we be willing to pay for an option to buy Netscape for 50 after the court case is over? Answer this question two ways: (i) find a probability distribution so that the two stocks are martingales, (ii) show that by using cash and buying Microsoft and Netscape stock one can replicate the option. 6.6. Consider the two-period binomial model with u = 2, d = 1/2 and interest rate r = 1/4. and suppose S0 = 100. What is the value of the European call option with strike price 80, i.e., the option with payo↵ (S2 80)+ . Find the stock holdings 0 , 1 (H ) and 1 (T ) need to replicate the option exactly. 6.7. Consider the two-period binomial mo...
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