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Review of Discrete and Continuous Processes in Finance: Theory and Applications

33 Pages Posted: 5 Apr 2009 Last revised: 6 Dec 2010

Attilio Meucci

ARPM - Advanced Risk and Portfolio Management

Date Written: July 1, 2009

Abstract

We review the main processes used to model financial variables. We emphasize the parallel between discrete-time processes, mainly used by econometricians for risk- and portfolio-management, and their continuous-time counterparts, mainly used by mathematicians to price derivatives. We highlight the relationship of such processes with the building blocks of stochastic dynamics and statistical inference, namely the invariants. Figures and practical examples support intuition. Fully documented code illustrating these processes in practice is available for download

Keywords: invariants, random walk, Levy processes, autocorrelation, ARMA, Ornstein-Uhlenbeck, Heston, CIR, jumps, long memory, fractional integration, fractional Brownian motion, volatility clustering, GARCH, stochastic volatility, subordination, real measure, risk-neutral measure, fat tails

JEL Classification: C1, G11

Suggested Citation

Meucci, Attilio, Review of Discrete and Continuous Processes in Finance: Theory and Applications (July 1, 2009). Available at SSRN: https://ssrn.com/abstract=1373102 or http://dx.doi.org/10.2139/ssrn.1373102

Attilio Meucci (Contact Author)

ARPM - Advanced Risk and Portfolio Management ( email )

HOME PAGE: http://www.arpm.co/

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