Stochastic

We cannot achieve any yi theorem 65 implies that our

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Unformatted text preview: H ) Sn+1 (aH ) Vn+1 (aT ) Sn+1 (aT ) one needs all of the information generated by the recursion. 2 (HH ) =0 2 (HT ) = (0 (T T ) = (6 2 1 (H ) = (0 6)/(16 4) = 0.5 9)/(4 1) = 1 2.4)/(32 8) = 0.1 1 (T ) = (2.4 6)/(8 2) = 0.6 3.2)/(16 4) 0 (T ) = (0.96 Notice that Vn (aH ) Vn (aT ) and the change in the price of the option is always smaller than the change in the price of the stock so 1 n (a) 0. 190 CHAPTER 6. MATHEMATICAL FINANCE Example 6.4. Put-call parity. Consider the binomial model with S0 = 32, u = 3/2, d = 2/3 and r = 1/6. By (6.5) the risk neutral probability p⇤ = 1+r d 7/6 = ud 3/2 2/ 3 3/ 6 = = 0.6 2/3 5/ 6 so by (6.12) the value satisfies Vn (a) = 1 (3.6Vn+1 (aH ) + 2.4Vn+1 (aT )) 7 We will now compute the values for the call and put with strike 49 and expiry 2. In the diagrams below the numbers above the line are the value of the stock and the ones below are the value of the option, and the replicating strategy. 81 call 32 54 115.2 A 7 A 36 A 414.72 A 49 A A put 36 A A A 31.2 7 414.72 A 49 0 54 36 0 24 0 81 A A A 36 13 24 126 7 16...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

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