Efficient Construction of Particle Filters for Continuous Time Finance Models

• Activity Number: 236
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Michael K. Pitt*+
• Companies: University of Warwick
• Keywords: particle filter ; stochastic differential equation ; simulation ; finance ; stochastic volatility

Abstract

Particle filters provide a convenient method for analyzing discrete time models. Recently, these simulation filters have also been considered for continuous time models. General stochastic differential equations are considered, in which a component of the multivariate series is considered observed at discrete time intervals. These models are known as partially observed diffusions. Such models include continuous time stochastic volatility models for stock prices and interest rates. In this paper it is shown that discretization via the Euler method can lead to particle filter methods which become increasingly inefficient as the discretization becomes more fine. The first models considered are partially observed models which have a strong solution, conditional upon the latent components of the model. Examples of such models are the standard models of stock prices with stochastic volatility. In this case methods are discussed which are invariant in efficiency to the fineness of the Euler discretization. This is demonstrated by considering a stochastic volatility example. Invariant methods are then considered for more general partially observed diffusions.