Derivative Securities – Fall 2007– Section 4 Notes
نویسنده
چکیده
Lognormal price dynamics and passage to the continuum limit. After a brief recap of our pricing formula, this section introduces the lognormal model of stock price dynamics, and explains how it can be approximated using binomial trees. Then we use these binomial trees to price contingent claims. The Black-Scholes analysis is obtained in the limit δt→ 0. As usual, Baxter–Rennie captures the central ideas concisely yet completely (Section 2.4). Hull has a lot of information about the lognormal model scattered through Chapter 13.
منابع مشابه
Derivative Securities – Fall 2007– Section 7 Notes
which is a Riemann sum for ∫ b a g 2(s) ds. By the way: since we are assuming that g is deterministic, ∫ b a g(s)dw(s) is a Gaussian random variable. (Proof: recall that a sum of Gaussians is Gaussian; therefore ∑ i g(si)[w(si+1) − w(si)] is Gaussian. Now use the fact that a limit of Gaussians is Gaussian.) Since we know its mean and variance, we have completely characterized this random variable.
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