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Estimation of a Self-Exciting Poisson Jump Diffusion Model by the Empirical Characteristic Function Method

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  • Yu, Jun

Abstract

This paper proposes a new econometric methodology for the estimation of diffusion models that include a jump component. The jump component's arrival time is endogenously determined, reflecting past volatility in the data and deviations from economic fundamentals. Although the likelihood method does not have closed form for this model, we show that the characteristic function can be derived analytically and hence developed an empirical characteristic function method to estimate the system parameters. This procedure has the same asymptotic efficiency as maximum likelihood, and is thus a desirable method to use when the likelihood function is unknown. A Monte Carlo study shows that the empirical characteristic function method outperforms the GMM procedure for the model. An application is considered for S&P 500 daily returns.

Suggested Citation

  • Yu, Jun, 1999. "Estimation of a Self-Exciting Poisson Jump Diffusion Model by the Empirical Characteristic Function Method," Working Papers 168, Department of Economics, The University of Auckland.
    • Handle: RePEc:auc:wpaper:168
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    File URL: http://hdl.handle.net/2292/168
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