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 Cheyette [1] — to a “minimal” form in which the swap rate evolves essentially like a dividend-paying stock. Using a number of numerical examples we compare such a minimal “poor man’s” model to a full-fledged Cheyette local volatility model and the market benchmark Hull–White one-factor model. Numerical tests demonstrate that the “poor man’s” model is in fact sufficient to price Bermudan 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.