Continuous-Time Models for Financial Time Series

Abstract

Many stochastic models in modern finance are represented in continuous-time. In these models, the dynamic behavior of the underlying random factors is often described by a system of stochastic differential equations (SDEs). The leading example is the option pricing model of Black and Scholes (1973), in which the underlying stock price evolves according to a geometric SDE. For asset pricing purposes, continuous-time financial models are often more convenient to work with than discrete-time models. For practical applications of continuous-time models, it is necessary to solve, either analytically or numerically, systems of SDEs. In addition, the simulation of continuous-time financial models is necessary for estimation using the Efficient Method of Moments (EMM) described in Chapter 23. This chapter discusses the most common types of SDEs used in continuous-time financial models and gives an overview of numerical techniques for simulating solution paths to these SDEs.