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Approximation of A Jump-Diffusion Process

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  • Sanghoon Lee

Abstract

We present a weak convergence of a discrete time process to a jump-diffusion process as the length of sampling interval, h, goes to zero. There is an example given for the weak convergency with using GARCH (1,1)-M model by Engle and Bollerslev(1986). It is shown that ARCH type models can be used as discrete time approximations of jump-diffusion processes. We use Exponential ARCH with Poisson Jump component as an example for the approximation. Therefore, we may use a discrete time ARCH process as an approximation of a jump-diffusion process in estimation and forecasting. And we may use the jump-diffusion process as an approximation of ARCH process when there is distributional results available for the jump-diffusion limit of the sequence of ARCH processes

Suggested Citation

  • Sanghoon Lee, 2004. "Approximation of A Jump-Diffusion Process," Econometric Society 2004 Far Eastern Meetings 412, Econometric Society.
    • Handle: RePEc:ecm:feam04:412
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    More about this item

    Keywords

    Weak Convergence; ARCH Type Models; Jump-Diffusion Process;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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