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.
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