On the Bayesian estimation of jump-diffusion models in finance

The jump-diffusion framework introduced by Duffie et al. (2000) encompasses most one factor models used in finance. Due to the model complexity of this framework, the particle filter (e.g., Hurn et al., 2015; Jacobs & Liu, 2018) and combinations of Gibbs and Metropolis-Hastings samplers (e.g., Eraker et al., 2003; Eraker, 2004) have been the tools of choice for its estimation. However, Bégin & Boudreault (2020) recently showed that the discrete nonlinear filter (DNF) of Kitagawa (1987) can also be used for fast and accurate maximum likelihood estimation of jump-diffusion models. In this project report, we combine the DNF with Markov chain Monte Carlo (MCMC) methods for Bayesian estimation in the spirit of the particle MCMC algorithm of Andrieu et al. (2010). In addition, we show that derivative prices (i.e., European option prices) can be easily included into the DNF's likelihood evaluations, which allows for efficient joint Bayesian estimation.