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Recursive Estimation for Continuous Time Stochastic Volatility Models Using the Milstein Approximation

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DOI: 10.4236/jmf.2013.33036    2,804 Downloads   4,621 Views  

ABSTRACT

Optimal as well as recursive parameter estimation for semimartingales had been studied in [1,2]. Recently, there has been a growing interest in modelling volatility of the observed process by nonlinear stochastic processes [3]. In this paper, we study the recursive estimates for various classes of discretely sampled continuous time stochastic volatility models using the Milstein approximation. We provide closed form expressions for the recursive estimates for recently proposed stochastic volatility models. We also give an example of computation of the term structure of zero rates in an incomplete information environment. In this case, learning about an unobserved state variable is done jointly with the valuation procedure.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

T. Koulis, A. Paseka and A. Thavaneswaran, "Recursive Estimation for Continuous Time Stochastic Volatility Models Using the Milstein Approximation," Journal of Mathematical Finance, Vol. 3 No. 3, 2013, pp. 357-365. doi: 10.4236/jmf.2013.33036.

References

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