Long-Memory Stochastic Volatility Models: A New Method for Inference and Applications in Option Pricing

Stochastic volatility (SV) models play an important role in finance. Under these models, the volatility of an asset follows an individual stochastic process. In contrast to the GARCH model, the volatility process in the SV model is autonomous with no need to refer to the asset price. It is often assumed that the log-volatility process follows a standard ARMA process in an SV model. However, empirical evidence indicates that the volatility of many assets has the “long-memory” property, which means that the autocorrelation of the volatility decays slower than exponentially as it does in an ARMAtype process. One way to incorporate this property into the SV model is by allowing the log-volatility to follow a fractionally integrated ARMA (ARFIMA) process. Such a model is called a long-memory stochastic volatility (LMSV) model. A large part of this research is focused on developing a new inference method via the sequential Monte Carlo (SMC) algorithm to estimate parameters in the LMSV model. In addition, we will check the “goodness-of-fit” of the model by comparing the LMSV model with other models based on the likelihood and other criteria. As an alternative method of model comparison, we can also price certain financial instruments, such as stock options, with our model and compare the results with the real market price and results based on other models.