Stochastic Volatility

Although it was recognised many decades ago that financial markets are characterised by volatility which changes over time, it has only been in the last 20 years or so that a large interest has been shown by econometricians in time series models with time‐varying volatility. Undoubtedly, this was mainly due to Robert Engle’s seminal 1982 work on ARCH processes, which model the risky part of returns as the product process where ɛt is a martingale difference with unit conditional variance and (the conditional variance of the return) is a random variable measurable with respect to the past information set, say It−1. A drawback of the ARCH class of models is that they do not link in well with the large body of continuous time models widely used in financial economics, e.g., to price derivatives. However, a different interpretation, much closer to modern finance theory, can be given to the product process in (1). In particular, σt might be viewed as being generated by an unobserved stochastic process (e.g., a latent autoregression), and not necessarily It−1‐measurable. This assumption defines a class of models, which permit one to specify a separate stochastic process for volatility without having to worry about the implied distribution of the returns; this is what is referred to as the class of ‘stochastic volatility’ [SV] models, and it is to this class of processes that Neil Shephard has dedicated this volume of readings

Autoregressive conditional heteroskedasticity · Conditional variance · Econometrics · Economics · Financial economics · Implied volatility · Martingale (probability theory) · SABR volatility model · Statistics · Stochastic volatility · Variance swap · Volatility (finance · Complex Systems and Time Series Analysis · Financial Risk and Volatility Modeling · Market Dynamics and Volatility · Mathematics