1 - Volatility modelling and forecasting in finance

Abstract

Volatility modeling and forecasting have attracted much attention in recent years, largely motivated by its importance in financial markets. Many asset-pricing models use volatility estimates as a simple risk measure, and volatility appears in option pricing formulas derived from such models. For hedging against risk and for portfolio management, reliable volatility estimates and forecasts are crucial. To account for different stylized facts, several types of models are available such as autoregressive moving average (ARMA) models, autoregressive conditional heteroscedasticity (ARCH) models, stochastic volatility (SV) models, regime switching models, and threshold models. One of the important shortcomings of the ARMA-type models is the assumption of constant variance. Most financial data exhibit changes in volatility, and this feature of the data cannot by captured under this assumption. An important property of ARCH models is their ability to capture volatility clustering in financial data. The idea behind the regime switching model is that the data that show changes in the regime will repeat themselves in the future. Therefore one can predict future states by using the parameter estimates from past observations. Stochastic variance or stochastic volatility models lead to the generalizations of the well-known Black–Scholes results in finance theory, in addition to many other applications.