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

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.

Keywords:

• mean reverting model with time-dependent volatility
• Black–Scholes model
• inverse problem of option pricing
• volatility calibration
• Maximum likelihood estimation

2000 AMS Subject Classifications :

• 60G15
• 65J15
• 62M10