Swap Rate à la Stock: Bermudan Swaptions Made Easy

Abstract

We show how Markovian projection, together with some clever parameter freezing, can be used to reduce a full-fledged local volatility interest rate model – such as the Cheyette model – to a “minimal” form in which the swap rate evolved essentially like a dividend-paying stock. Using a number or numerical examples, we compare such a minimal “poor man's” model to a full-fledged Cheyette local volatility model and the market benchmark Hall–White one-factor model. Numerical tests demonstrate that the “poor man's” model is in fact sufficient to price Bermudian interest rate swaptions. The main practical implication of this finding is that – once local volatility, dividend, and short rate parameters are properly stripped from the volatility surface and interest rate curve – one can readily use the widely popular equity derivatives software for pricing exotic interest rate options such as Bermudans.