Quantitative Financial Risk Management: Theory and Practice

CHAPTER 4

A Practical Guide to Regime Switching in Financial Economics

Iain Clacher

Leeds University, UK

Mark Freeman

Loughborough University, UK

David Hillier

University of Strathclyde, UK

Malcolm Kemp

Nematrian Limited, UK

Qi Zhang

Leeds University, UK

A standard assumption in empirical finance is that logarithmic returns to a number of financial asset classes are independently and identically normally distributed (i.i.n.d.). This is convenient to work with analytically and underlies a number of the key theorems in asset pricing, including the Black–Scholes–Merton options pricing model. A further assumption is also commonly invoked that restricts the correlations between different financial assets to be constant over time. This, again, aids in determining closed-form solutions to optimal asset allocation problems.

Despite the mathematical appeal of this framework, it is well known that it does not accurately capture the real-world dynamics of asset returns. There are extensive literatures that document time-varying expected returns, time-varying volatility (heteroskedasticity), autocorrelation, fat-tailed distributions where outliers occur considerably more frequently than might be estimated under the assumption of normality (leptokurtosis), and time-variation in cross-sectional correlation when describing the actual price behavior of financial assets.

Markov regime switching models are one of a range of statistical techniques that capture these observed characteristics of asset ...