Swap Rate à la Stock: Bermudan Swaptions Made Easy

D. Gatarek and J. Jabłecki

Chapter 18 in Options — 45 Years since the Publication of the Black–Scholes–Merton Model:The Gershon Fintech Center Conference, 2023, pp 393-412 from World Scientific Publishing Co. Pte. Ltd.

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 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.

Keywords: Options; Call; Put; Stock; Equity; Bond; Debt; Dividend; Investment; Diversification; Volatility; Black–Scholes; Merton Model; Stochastic; Swap; Commodity; Index; Contingent Claims; Exotic Option (search for similar items in EconPapers)
JEL-codes: C C02 G1 G11 G12 G15 (search for similar items in EconPapers)
Date: 2023
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