Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 63. Introduction to Stochastic Processes

SVETLOZAR T. RACHEV, PhD, DrSci

Chair-Professor, Chair of Econometrics, Statistics Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and Department of Statistics and Applied Probability University of California, Santa Barbara

CHRISTIAN MENN, Dr. rer. pol.

Associate, Sal. Oppenheim Jr. & Cie, Frankfurt, Germany

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

Abstract: In financial modeling, practitioners draw upon tools in the field of mathematics. In asset return modeling, option pricing modeling, term structure modeling, and credit risk modeling, the primary mathematical tool used by practitioners is stochastic processes which concerns sequences of events that are governed by the laws of probability. When the sequence of events for a stochastic process involves data points measured at successive time intervals, the sequence is referred to as a time series. Practitioners seek to understand the behavior of a financial time series so that they can forecast or predict future returns based on past returns. Stochastic processes involving time series can be classified as discrete-time stochastic processes and continuous-time stochastic processes.

Keywords: stochastic process, discrete-time stochastic process, continuous-time stochastic process, autoregressive moving average, white noise process, autoregressive process, autocorrelation function, partial autocorrelation ...