# 617 continuing with the model of previous problem s0

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Unformatted text preview: ( t ↵) = ( t ↵) of a where in the middle equality we have used the fact that and have the same distribution. Using the last two computations in (6.33) converts it to rt e Now e normal r t µt ee 2 t/2 S0 eµt e 2 t/2 ( = 1 since µ = r d1 = p t ↵= p ↵) t 2 e rt K ( ↵) /2. As for the argument of the ﬁrst log(S0 /K ) + (r p t 2 /2)t + p t which agrees with the formula given in the theorem. The second one is much p easier to see: d2 = d1 t. Example 6.9. A Google call options. On the morning of December 5, 2011 Google stock was selling for \$620 a share and a March 12 call option with strike K = 635 was selling for \$33.10. To compare this with the prediction of the Black-Scholes formula we assume an interest rate of r = 0.01 per year and assume a volatility = 0.3. The 100 days until expiration of the option are t = 0.27393 years. With the help of a little spreadsheet we ﬁnd that the formula predcits a price of \$32.93. 203 6.8. EXERCISES Example 6.10. Put-call parity allows us to compute the value of the putoption, VP from the...
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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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