The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

CHAPTER 6

Modeling Asset Price Dynamics

Dessislava A. Pachamanova, Ph.D. Associate Professor of Operations Research Babson College

 

Frank J. Fabozzi, Ph.D., CFA, CPA Professor in the Practice of Finance Yale School of Management

 

 

 

 

 

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. In this chapter, we present 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.

In this chapter, we introduce the fundamentals of binomial tree and random walk models, providing examples for how they can be used in practice. We briefly discuss the special notation and terminology associated with stochastic processes at the end of this chapter; however, our focus is on interpretation and simulation of processes in discrete time. The roots for the techniques we describe are in physics and the other natural sciences. They were first applied in finance at the beginning of the twentieth century, and have represented the foundations of asset pricing ever since.