19 however from the new solution we can easily see

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Unformatted text preview: A A A A 0 A 16 33 We have written the values as fractions to make it clear that the value at time 0 of these two options are exactly the same. Once you realize this it is easy to prove. Theorem 6.6. The values VP and VC of the put and call options with the same strike K and expiration N are related by VP VC = K (1 + r)N S0 In particular if K = (1 + r)N S0 then VP = VC . Proof. The key observation is that SN + (K SN )+ (SN K )+ = K Consider the two cases SN K and SN K . Dividing by (1 + r)N , taking E ⇤ expected value and using the fact that Sn /(1 + r)n is a martingale S0 + E ⇤ (K SN )+ (1 + r)N E⇤ (K SN )+ K = (1 + r)N (1 + r)N Since the second term on the left is VP and the third is VC the desired result follows. 191 6.4. CAPITAL ASSET PRICING MODEL It is important to note that the last result can be used to compute the value of any put from the corresponding call. Returning to the previous example and looking at the time 1 node where the price is 54, the formula above says 31.2 7 115.2 84 6 = =...
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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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