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The Stochastic Differential Equation

In: Derivative Security Pricing

Author

Listed:
  • Carl Chiarella

    (University of Technology Sydney)

  • Xue-Zhong He

    (University of Technology Sydney)

  • Christina Sklibosios Nikitopoulos

    (University of Technology Sydney)

Abstract

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.

Suggested Citation

  • Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "The Stochastic Differential Equation," Dynamic Modeling and Econometrics in Economics and Finance, in: Derivative Security Pricing, edition 127, chapter 0, pages 55-91, Springer.
  • Handle: RePEc:spr:dymchp:978-3-662-45906-5_4
    DOI: 10.1007/978-3-662-45906-5_4
    as

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