November 2012
Beginner
733 pages
27h 41m
English
Content preview from Encyclopedia of Financial Models III
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Stochastic Processes in Continuous Time
Abstract: The dynamic of a financial asset's returns and prices can be expressed using a deterministic process if there is no uncertainty about its future behavior, or with a stochastic process in the more likely case when the value is uncertain. Stochastic processes in continuous time are the most used tool to explain the dynamics of a financial asset's returns and prices. They are the building blocks with which to construct financial models for portfolio optimization, derivatives pricing, and risk management. Continuous-time processes allow for more elegant theoretical modeling compared to discrete-time models and many results proven in probability theory can be applied to obtain a simple evaluation method.
In 1900, the father of modern option pricing theory, Louis Bachelier, proposed using Brownian motion for modeling stock market prices. There are several reasons why Brownian motion is a popular process. First, Brownian motion is the milestone ...