Volatility Processes

Archil Gulisashvili
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Archil Gulisashvili: Ohio University

Chapter Chapter 1 in Analytically Tractable Stochastic Stock Price Models, 2012, pp 1-36 from Springer

Abstract: Abstract The book begins with an overview of the properties of several stochastic processes that play an important role in modeling of the volatility of the stock. The family of volatility processes includes Brownian motion, geometric Brownian motion, Ornstein-Uhlenbeck processes, squared Bessel processes, and Cox-Ingersoll-Ross processes (CIR-processes). In the first chapter, means and variances of these processes are computed and marginal distributions associated with the volatility processes are found. For a geometric Brownian motion, marginal distributions are log-normal, for an Ornstein-Uhlenbeck process, they are Gaussian, while for a CIR-process, they coincide with noncentral chi-square distributions. The chapter also includes the proof of the Pittman-Yor theorem. This theorem concerns certain exponential functionals of squared Bessel processes.

Keywords: Brownian Motion; Stock Price; Stock Return; Stochastic Differential Equation; Marginal Distribution (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-642-31214-4_1

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DOI: 10.1007/978-3-642-31214-4_1

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