Bifactorial Pricing Models: Light and Shadows in Correlation Role

Abstract

In modern option pricing theory many attempts have been accomplished in order to release some of the traditional assumptions of the Black and Scholes [5] model. Distinguished in this field are models allowing for stochastic interest rates, as suggested for the first time by Merton [20]. Afterwards, many stochastic interest rate models to evaluate the price of hybrid securities have been proposed in literature. Most of these are equilibrium pricing models whose parameters are estimated by means of statistical procedure, requiring a considerable computational burden. The recent financial crisis and the resulting instability of relevant time series may sensibly reduce the reliability of estimated parameters necessary to such models and, consequently, the calibration of the models. In this paper we discuss an original numerical procedure that can efficiently be adopted to the aim of pricing and the question of the correlation contribution in pricing framework. The procedure accounts for two sources of risk (the stock price and the spot interest rate) and, by means of an empirical evaluation tries to asses the relative contribution of the correlation component. The final target is to evaluate the “optimal” computation burden in pricing framework, given scarce dataset We show that the procedure proposed is a valuable compromise between computational burden and calibration efficiency, mainly because it overcomes difficulties and arbitrary choices in the estimation of the parameters.