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 and the interest rate dynamics by the Hull-White short-rate model. We propose a projection formula, mapping the SABR-HW model parameters onto the parameters of the nearest SABR model. A time-dependent parameter extension of this SABR-HW model is adopted to make the calibration of the model consistent across maturity times. The calibration procedure is then finalized by employing the weighted Monte Carlo technique. The Monte Carlo weights are not uniform and chosen to replicate the calibration market instruments