The Stochastic Differential Equation

Carl Chiarella*, Xue Zhong He, Christina Sklibosios Nikitopoulos

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingChapterpeer-review


To develop the hedging argument of Black and Scholes, this chapter introduces stochastic differential equations to model the evolution of the price path itself and the statistical properties of small price changes over small changes in time. We then consider the stochastic differential equations for the Wiener process, Ornstein–Uhlenbeck process and Poisson process and examine the autocovariance behaviour of the Wiener process. Furthermore we introduce stochastic integrals to define the stochastic differential equations.

Original languageEnglish
Title of host publicationDynamic Modeling and Econometrics in Economics and Finance
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages37
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameDynamic Modeling and Econometrics in Economics and Finance
ISSN (Print)1566-0419
ISSN (Electronic)2363-8370


  • Planck Equation
  • Price Change
  • Sample Path
  • Stochastic Differential Equation
  • Wiener Process


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