Swap Rate à la Stock: Bermudan Swaptions Made Easy

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.