Discrete nonlinear filtering in finance: Applications to stochastic volatility jump-diffusion models

Abstract

Over the past thirty years, stochastic volatility jump-diffusion models have been widely used as they can reproduce some important stylized facts. Yet parameter estimation for these models is cumbersome because the variance process and the jumps are not directly observed. In this presentation, we first present a deterministic discrete nonlinear filtering algorithm based on a high-dimensional version of Kitagawa (1987) to evaluate the likelihood function of models that allow for stochastic volatility and jumps. We show numerically that the discrete nonlinear filter (DNF) is precise and much faster than the particle filter, in addition to yielding a smooth function over the parameter set. Moreover, we provide a brief overview of the SVDNF R package, which makes the DNF available to other researchers and users. Second, this new implementation of the DNF allows us to investigate the behaviour of the maximum likelihood estimator (MLE) for this class of models. We find that the MLE is unable to replicate key higher moments based on real data from nine indices and more than 6,000 individual stocks. To fix this issue, we then introduce a moment-targeted MLE—robust to model misspecification. This is joint work with Louis Arsenault-Mahjoubi and Mathieu Boudreault.