ESTIMATION IN CONTINUOUS-TIME STOCHASTIC VOLATILITY MODELS USING NONLINEAR FILTERS

Jan Nygaard Nielsen () and Martin Vestergaard ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2000, vol. 03, issue 02, 279-308

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.

Keywords: Stochastic volatility; volatility estimation; nonlinear filtering; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1142/S0219024900000139

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