Stochastic

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Unformatted text preview: ce of 0.4 for a put with strike 33 consistent with put-call parity. 206 CHAPTER 6. MATHEMATICAL FINANCE 6.25. On December 20, 2011, stock in Exxon Mobil was selling at 81.63. (a) Use the Black-Scholes formula to compute the value of an April 12 call (t = 0.3123 years) with strike 70, assuming an interest rate of r = 0.01 and the volatility = 0.26. The volatility here has been chosen to make the price consistent with the bid-ask spread of (12.6,12.7). (b) Is the price of 1.43 for a put with strike 70 consistent with put-call parity. Appendix A Review of Probability Here we will review some of the basic facts usually taught in a ﬁrst course in probability, concentrating on the ones that are important in the book. A.1 Probabilities, Independence The term experiment is used to refer to any process whose outcome is not known in advance. Two simple experiments are ﬂip a coin, and roll a die. The sample space associated with an experiment is the set of all possible outcomes. The sample space is us...
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