Abstracts

In this short note we demonstrate that in a wide class of Equity-Interest rate hybrid models the price of an American put decreases when the interest rate volatility is increased. Specifically we consider models where the equity volatility is local in the spot price and the spot-rate correlation is non-negative. It is imperative that we stay within the calibrated set of models and that for any choice of the interest rate volatility the model is re-calibrated to match the vanillas. As a corollary we deduce that the maximum price of an American put within the specified set of models is achieved when the interest rate volatility goes to zero and the underlying model reduces to the local volatility model of Dupire. The result holds for the Bermudan option as well.