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Estimation In Continuous-Time Stochastic Volatility Models Using Nonlinear Filters

Author

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  • JAN NYGAARD NIELSEN

    (Department of Mathematical Modelling, Technical University of Denmark, Build. 321, DK-2800 Lyngby, Denmark)

  • MARTIN VESTERGAARD

    (Department of Mathematical Modelling, Technical University of Denmark, Build. 321, DK-2800 Lyngby, Denmark)

Abstract

The stylized facts of stock prices, interest and exchange rates have led econometricians to propose stochastic volatility models in both discrete and continuous time. However, the volatility as a measure of economic uncertainty is not directly observable in the financial markets. The objective of the continuous-discrete filtering problem considered here is to obtain estimates of the stock price and, in particular, the volatility using discrete-time observations of the stock price. Furthermore, the nonlinear filter acts as an important part of a proposed method for maximum likelihood for estimating embedded parameters in stochastic differential equations. In general, only approximate solutions to the continuous-discrete filtering problem exist in the form of a set of ordinary differential equations for the mean and covariance of the state variables. In the present paper the small-sample properties of a second order filter is examined for some bivariate stochastic volatility models and the new combined parameter and state estimation method is applied to US stock market data.

Suggested Citation

  • Jan Nygaard Nielsen & Martin Vestergaard, 2000. "Estimation In Continuous-Time Stochastic Volatility Models Using Nonlinear Filters," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 279-308.
    • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:02:n:s0219024900000139
    DOI: 10.1142/S0219024900000139
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    Cited by:

    1. Arenas, Zochil González & Jimenez, Juan Carlos & Lozada-Chang, Li-Vang & Santana, Roberto, 2021. "Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 449-467.
    2. Florescu, Ionuţ & Pãsãricã, Cristian Gabriel, 2009. "A study about the existence of the leverage effect in stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 419-432.

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