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Stochastic Processes in Finance

Author

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  • Dilip B. Madan

    (Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

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.

Suggested Citation

  • Dilip B. Madan, 2010. "Stochastic Processes in Finance," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 277-314, December.
    • Handle: RePEc:anr:refeco:v:2:y:2010:p:277-314
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    File URL: http://www.annualreviews.org/doi/abs/10.1146/annurev.financial.050808.114506
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    Cited by:

    1. Buckley, Winston & Long, Hongwei & Marshall, Mario, 2016. "Numerical approximations of optimal portfolios in mispriced asymmetric Lévy markets," European Journal of Operational Research, Elsevier, vol. 252(2), pages 676-686.
    2. Grechuk, Bogdan & Zabarankin, Michael, 2018. "Direct data-based decision making under uncertainty," European Journal of Operational Research, Elsevier, vol. 267(1), pages 200-211.

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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