Software for quasi-likelihood and indirect inference in non-Gaussian stochastic volatility models for exchange rate data

The current financial crisis has led to renewed interest in the topic of volatility modelling. Standard Gaussian models, such as the celebrated Black-Scholes-Merton model, may not be appropriate and the need for implementing more realistic models of risk seems more important than ever

We aim to contribute to this research by a new method for inference (estimation and prediction) in stochastic volatility models for exchange rate data based on non-Gaussian Ornstein-Uhlenbeck (OU) processes. Our approach uses an indirect inference method: First, an auxiliary model based on an approximate linear state space representation of the OU-based model is estimated. Then simulations are made from the underlying OU-model for given parameter values. A method of moments version of indirect inference is implemented: The indirect inference estimator is the parameter value in the OU-model which minimizes, in a weighted mean squared error sense, the score vector of the quasi-likelihood function for the simulated data, when this score vector is evaluated at the quasi-likelihood estimator obtained from the real data. A simulation study reveals that the quasi-likelihood estimator may have a large bias even in large samples, but that the indirect inference estimator either eliminates or substantially reduces this bias. The indirect inference and the quasi likelihood method are documented in the following discussion paper:
Indirect inference methods for stochastic volatility models based on non-Gaussian Ornstein- Uhlenbeck processes and in the supplementary document:
The derivatives of the log-likelihood for the Gaussian state space model

We also considered a multivariate extension of the univariate stochastic volatility model. Despite the fact that multivariate modeling of asset returns is essential for portfolio optimization and risk management -- major areas of financial analysis -- the literature on multivariate modeling of asset prices in continuous time is sparse, both with regard to theoretical and applied results. We show that a computationally feasible quasi-likelihood function can be constructed by means of the Kalman filter also in the case of high-dimensional vector processes. This multivariate approach is documented in the discussion paper:
Multivariate stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck processes -- A quasi-likelihood approach.

A first version of an R package, with interface to efficient C++ code, have implemented these methods. It does both indirect inference (for the univariate case) and quasi likelihood estimation (univariate and bivariate). The software may be downloaded from The Comprenhensive R Archive Network (CRAN). Here is an univariate example data file and a bivariate example data file. A getting started manual may also be downloaded. The software is developed by Arvid Raknerud arvid.raknerud@ssb.no and Øivind Skare.