Stochastic Volatility Estimation Using Markov Chain Simulation

Stochastic volatility (SV) models are workhorses for the modelling and prediction of time-varying volatility on financial markets and are essential tools in risk management, asset pricing and asset allocation. In financial mathematics and financial economics, stochastic volatility is typically modeled in a continuous-time setting which is advantageous for derivative pricing and portfolio optimization. Nevertheless, since data is typically only observable at discrete points in time, in empirical applications, discrete-time formulations of SV models are equally important.

The main objective of this chapter is to present the most important specifications of discrete-time SV models, to illustrate the major principles of Markov Chain Monte Carlo (MCMC) based statistical inference, and to show how to implement these techniques to estimate SV models. In this context, we provide a hands-on approach which is easily extended in various directions. Moreover, we will illustrate empirical results based on different SV specifications using returns on stock indices and foreign exchange rates.