Sequential Bayesian Analysis of Time-Changed Infinite Activity Derivatives Pricing Models

Abstract

This paper investigates time-changed infinite activity derivatives pricing models from the sequential Bayesian perspective. It proposes a sequential Monte Carlo method with the proposal density generated by the unscented Kalman filter. This approach overcomes to a large extent the particle impoverishment problem inherent to the conventional particle filter. Simulation study and real applications indicate that (1) using the underlying alone cannot capture the dynamics of states, and by including options, the precision of state filtering gets improved dramatically; (2) the proposed method performs better and is more robust than the conventional one; (3) the joint identification of the diffusion, stochastic volatility and jumps can be achieved using both the underlying and options data.

Keywords: Infinite Activity Levy Processes, Brownian Subordination, Stochastic Volatility, Unscented Kalman Filter, Sequential Monte Carlo

JEL Classification: C11, C13, C32, G13