Cash-Settled Swaptions: A New Pricing Model

Abstract

The market for cash-settled swaptions has changed its quotation conventions. Cash-settled zero-wide collars struck at the swap-settled forward have started trading at non-zero prices. Apart from full- fledged term-structure models, a simple arbitrage-free model to consistently value both cash-settled and swap-settled swaptions has been lacking so far. We propose a straightforward arbitrage-free model that consistently values cash-settled and swap-settled swaptions, and that also allows to match the newly published zero-wide collar premiums. The defining characteristic of the model is to explicitly specify the swap-settled annuity as a function of a discount swap rate under the swap-settled annuity measure. The new methodology has many desirable features, and a numerical example illustrates how the model performs in realistic market scenarios.

Keywords: Cash-Settled Swaption, Zero-Wide Collar, Black Model, Bachelier Model, SABR, Shifted Log-Normal

JEL Classification: C51