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Numerical Solution of Stochastic Differential Equations in Finance

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Handbook of Computational Finance

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

This chapter is an introduction and survey of numerical solution methods for stochastic differential equations. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial systems. We include a review of fundamental concepts, a description of elementary numerical methods and the concepts of convergence and order for stochastic differential equation solvers. In the remainder of the chapter we describe applications of SDE solvers to Monte-Carlo sampling for financial pricing of derivatives. Monte-Carlo simulation can be computationally inefficient in its basic form, and so we explore some common methods for fostering efficiency by variance reduction and the use of quasi-random numbers. In addition, we briefly discuss the extension of SDE solvers to coupled systems driven by correlated noise, which is applicable to multiple asset markets.

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Author information

Authors and Affiliations

  1. Department of Mathematics, George Mason University, Fairfax, VA, 22030, USA

    Timothy Sauer

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  1. Timothy Sauer
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Correspondence to Timothy Sauer .

Editor information

Editors and Affiliations

  1. , Risk Management Institute, National University of Singapore, 21 Heng Mui Keng Terrace, Level 4, Singapore, 119613, Singapore

    Jin-Chuan Duan

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. , Department of Computational and Data Sci, George Mason University, University Drive 4400, Fairfax, 22030, Virginia, USA

    James E. Gentle

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Sauer, T. (2012). Numerical Solution of Stochastic Differential Equations in Finance. In: Duan, JC., Härdle, W., Gentle, J. (eds) Handbook of Computational Finance. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17254-0_19

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