P. E. Kloeden and E. Platen, “Numerical Solution of Stochastic Differential Equations,” Applications of Mathematics, Vol. 23, 1992, in press. doi:10.1007/978-3-662-12616-5

has been cited by the following article:

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

  AUTHORS: Theodoro Koulis, Alexander Paseka, Aerambamoorthy Thavaneswaran

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

  JOURNAL NAME: Journal of Mathematical Finance, Vol.3 No.3, August 15, 2013

  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.