Sequential Parameter Estimation in Stochastic Volatility Models with Jumps

This paper analyzes the sequential lear ning problem for both parameters and states in a stochastic volatility model with jumps. We extend two existing algorithms, Storvik’s (2002) particle fi ltering algorithm and Polson, Stroud and Muller’s (2003) practical fi ltering algorithm, to inc orporate jumps. We analyze the performance of these approaches using both simulate d and S&P 500 index return data. We fi nd that the particle fi lter provides more accurate sequential inference than the practical fi ltering approach. The di ff erences are minor using simulated data, but greater using S&P 500 index data as the adapted particle fi ltering algorithm we use e ffi ciently handles outliers. We analyze the implications of learning about jump parameters for option pricing and fi nd that parameter learning generates important implications for option pricing.

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