Abstract
Chapter 6 extends coverage of stochastic processes needed to develop the financial models, including those that derive from stochastic differential equations. The differential of a stochastic process and stochastic integration is defined. Relevant properties and essential theorems concerning these two operations are covered. The Radon–Nikodym derivative is covered in detail, with applications to both discrete binomial probability measures and continuous normal densities. The chapter presents essential tools for pricing securities following continuous stochastic process, including the Cameron–Martin–Girsanov theorem, the martingale representation theorem, and Itô’s lemma. Using Itô’s lemma, the solution to the primary stochastic differential equation for modeling securities (geometric Brownian motion) is derived.
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