Simulation Methods for Stochastic Differential Equations

Eckhard Platen ()

Chapter 21 in Handbook on Information Technology in Finance, 2008, pp 501-514 from Springer

Abstract: Abstract As one tries to build more realistic models in finance, stochastic effects need to be taken into account. In finance, the randomness in the dynamics is in fact the essential phenomenon to be modeled. More than hundred years ago, Bachelier used in (Bachelier 1900) what we now call Brownian motion or the Wiener process to model stock prices observed at the Paris Bourse. Einstein, in his work on Brownian motion, employed in (Einstein 1906) an equivalent construct. Wiener, then developed the mathematical theory of Brownian motion in (Wiener 1923). Itô laid in (Itô 1944) the foundation of stochastic calculus, which represents a stochastic generalization of the classical differential calculus. It allows to model in continuous time the dynamics of stock prices or other financial quantities. The corresponding stochastic differential equations (SDEs) generalize ordinary deterministic differential equations.

Keywords: Stochastic Differential Equation; Wiener Process; Stochastic Volatility; Stochastic Volatility Model; Strong Order (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-49487-4_21

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