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Simulated Likelihood Approximations for Stochastic Volatility Models

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  • Helle Sørensen

Abstract

. This paper deals with parametric inference for continuous‐time stochastic volatility models observed at discrete points in time. We consider approximate maximum likelihood estimation: for the kth‐order approximation, we pretend that the observations form a kth‐order Markov chain, find the corresponding approximate log‐likelihood function, and maximize it with respect to θ. The approximate log‐likelihood function is not known analytically, but can easily be calculated by simulation. For each k, the method yields consistent and asymptotically normal estimators. Simulations from a model based on the Cox–Ingersoll–Ross model are used for illustration.

Suggested Citation

  • Helle Sørensen, 2003. "Simulated Likelihood Approximations for Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 257-276, June.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:2:p:257-276
    DOI: 10.1111/1467-9469.00330
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    Cited by:

    1. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.

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