Bayesian computation in finance

In this paper we describe the challenges of Bayesian computation in Finance. We show that empirical asset pricing leads to a nonlinear non-Gaussian state space model for the evolutions of asset returns and derivative prices. Bayesian methods extract latent state variables and estimate parameters by calculating the posterior distributions of interest. We describe the use of direct estimation methods such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods based on particle filtering (PF). Our approach also allows for an on-line model assessment via sequential Bayes factors. We illustrate our approach in two examples. First, sequential inference for extracting latent stochastic volatility and jump states from daily data throughout the credit crisis of 2007–2008 and secondly, an equilibrium-based asset pricing model for SP500 put options.