Sequential Parameter Estimation in Stochastic Volatility Models with Jumps

Michael S. Johannes, Nicholas G. Polson, Jonathan R. Stroud

Columbia University, University of Chicago, and George Washington University

This paper analyzes the sequential learning problem for both parameters and states in a stochastic volatility model with jumps. We extend two existing algorithms, Storvik's (2002) particle filtering algorithm and Polson, Stroud and Muller's (2008) practical filtering algorithm, to incorporate jumps. We analyze the performance of these approaches using both simulated and S&P 500 index return data. We find that the particle filter provides more accurate sequential inference than the practical filtering approach. The differences are minor using simulated data, but greater using S&P 500 index data as adapted particle filtering algorithm we use efficiently handles outliers. We analyze the implications of learning about jump parameters for option priceing and find that parameter learning generates important implications for option pricing.

The manuscript is available in PDF format.