Encyclopedia of Financial Models I

Modeling Asset Price Dynamics

DESSISLAVA A. PACHAMANOVA, PhD

Associate Professor of Operations Research, Babson College

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: The dynamics of asset price processes in discrete time increments are typically described by two kinds of models: trees (lattices) and random walks. Arithmetic, geometric, and mean reverting random walks are examples of the latter type of models. When the time increment used to model the asset price dynamics becomes infinitely small, we talk about stochastic processes in continuous time. Models for asset price dynamics can incorporate different observed characteristics of an asset price process, such as a drift or a reversion to a mean, and are important building blocks for risk management and financial derivative pricing models.

Many classical asset pricing models, such as the capital asset pricing theory and the arbitrage pricing theory, take a myopic view of investing: They consider events that happen one time period ahead, where the length of the time period is determined by the investor. This entry presents apparatus that can handle asset dynamics and volatility over time. The dynamics of price processes in discrete time increments are typically described by two kinds of models: trees (such as binomial trees) and random walks. When the time increment used to model the asset price dynamics becomes infinitely small, we talk about stochastic processes in continuous time. ...