The Stochastic Differential Equation

Carl Chiarella, Xuezhong (Tony) He () and Christina Sklibosios Nikitopoulos
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Christina Sklibosios Nikitopoulos: University of Technology Sydney

Chapter Chapter 4 in Derivative Security Pricing, 2015, pp 55-91 from Springer

Abstract: 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.

Keywords: Stochastic Differential Equation; Price Change; Sample Path; Wiener Process; Planck Equation (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:dymchp:978-3-662-45906-5_4

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DOI: 10.1007/978-3-662-45906-5_4

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