Estimation in continuous-time stochastic volatility models using nonlinear filters. (English) Zbl 1154.91467

Nielsen, Jan Nygaard; Vestergaard, Martin

Int. J. Theor. Appl. Finance 3, No. 2, 279-308 (2000).

Summary: 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.

MSC:

91B28	Finance etc. (MSC2000)
60H15	Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

stochastic volatility; volatility estimation; nonlinear filtering, Monte Carlo simulation

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