Calibration and Monte Carlo Pricing of the SABR-Hull-White Model for Long-Maturity Equity Derivatives

We model the joint dynamics of stock and interest rate by a hybrid SABR-Hull- White model, in which the asset price dynamics are modeled by the SABR model [18] and the interest rate dynamics by the Hull-White short-rate model [19]. We propose a projection formula, mapping the SABR-HW model parameters onto the parameters of the nearest SABR model. Further a time-dependent parameter extension of this SABR-HW model is introduced to make the calibration of the model consistent across maturities. The inverse of the projection formula enables a rapid calibration of the model. As the calibration quality subjects to the approximation errors of the projection formula, we subsequently apply a non-parametric numerical calibration technique based on the non-uniformly weighted Monte Carlo technique [5] to improve the calibration. In this step, the Monte Carlo weights are not uniform and chose