Stochastic Processes in Finance

Dilip B. Madan ()
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Dilip B. Madan: Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742

Annual Review of Financial Economics, 2010, vol. 2, issue 1, 277-314

Abstract: Stochastic processes arising in the description of the risk-neutral evolution of equity prices are reviewed. Starting with Brownian motion, I review extensions to Lévy and Sato processes. These processes have independent increments; the former are homogeneous in time, whereas the latter are inhomogeneous. One-dimensional Markov processes such as local volatility and local Lévy are discussed next. Finally, I take up two forms of stochastic volatility that are due to either space scaling or time changing. An encompassing discrete-time model closes the presentation.

JEL-codes: G12 (search for similar items in EconPapers)
Date: 2010
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