FINS3635 Week 10 - B-S model(3)

FINS3635 Week 10 - B-S model(3) - The Black-Scholes Model...

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1 The Black-Scholes Model Brief introduction to stochastic processes (from Ch. 13 and focusing on the lecture notes) Markov process Wi FINS 3635 week 10 1 Wiener process Generalized Wiener process Ito process Modeling stock prices – Geometric Brownian Motion Black-Scholes-Merton model (reading:14.4-13.9, 14.11-14.12) Markov Process Markov process stochastic process for which only the present value of a variable is relevant for predicting FINS 3635 week 10 2 the future. The past history of the variable is irrelevant. Markov property of stock prices is consistent with the weak form of market efficiency. Wiener Process A Wiener process is a particular type of Markov stochastic process with mean change of zero and a variance rate of 1.0 per year. A variable z follows a Wiener process if it has the FINS 3635 week 10 3 A variable z follows a Wiener process if it has the following two properties: Property 1 : The change in z during a short period of time t is , where ~ (0,1). Property 2 : The value change of z for any two different short intervals of time are independent. This property implies that z follows a Markov process z t
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