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Original Articles

Some aspects of parameter identification in a mean reverting financial asset model with time-dependent volatility

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Pages 992-1008 | Received 15 Aug 2008, Accepted 04 Dec 2008, Published online: 01 Jun 2009
 

Abstract

The present paper deals with several aspects and procedures of identification in a financial market model with time-dependent volatility function and mean reverting stochastic drift term. For this term, an external source of randomness is permitted. In this context, the corresponding inverse problem of option pricing is considered. Here it is of importance that the classical Black–Scholes formula remains unaffected by the drift term. On the other hand, estimating the quadratic variation of the process, high-frequency asset price data are used directly for calibrating the volatility function. We suggest an estimator that is based on a projection on an orthonormal wavelet basis. Finally, classical maximum likelihood methods are applied to estimate the parameters included in the drift term.

2000 AMS Subject Classifications :

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