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

Theodoro Koulis, Alexander Paseka, Aerambamoorthy Thavaneswaran

Department of Accounting and Finance, University of Manitoba, Winnipeg, Canada.
Department of Statistics, University of Manitoba, Winnipeg, Canada.

DOI: 10.4236/jmf.2013.33036                

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.

Keywords

Recursive Estimation; Diffusion Processes; Interest Rate Models; Milstein Approximation

Conflicts of Interest

The authors declare no conflicts of interest.

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