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 twoperiod 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 twoperiod binomial mo...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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