For a very general example of a p probability let 1 2

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Unformatted text preview: swer for V0 by using V0 = E ⇤ (V3 /(1 + r)3 ). 6.10. Consider the three-period binomial model with u = 3, d = 1/2 and r = 1/3 and S0 = 16. The European prime factor option pays o↵ $1 for each factor in the prime factorization of the stock price at time 3 (when the option expires). For example, if the stock price is 24 = 23 31 then the payo↵ is 4 = 3+1. Find the no arbitrage price of this option. 6.11. Suppose S0 = 27, u = 4/3, d = 2/3 and interest rate r = 1/9. The European “cash-or-nothing option” pays $1 if S3 > 27 and 0 otherwise. Find the value of the option Vn and for the hedge n . 6.12. Assume the binomial model with S0 = 54, u = 3/2, d = 2/3, and r = 1/6. and consider a put (50 S3 )+ with a knockout barrier at 70. Find the value of the option. 6.13. Consider now a four period binomial model with S0 = 32, u = 2, d = 1/2, and r = 1/4, and suppose we have a put (50 S4 )+ with a knockout barrier at 100. Show that the knockout option as the same value as an option that pays o↵ (50 S4 )+ when S4 = 2, 8, or 32, 0 when S4 = 128, and 18 when S4 = 512. (b) Compute the value of the option in (a). 6.8. EXERCISES 205 6.14. Consider the binomial model with...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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