Pricing Swaptions in a Negative Interest Rate Environment

Specialeforsvar ved Mickey Zarp Klein Petersen

Titel: Pricing Swaptions in a Negative Interest Rate Environment

Abstract: In the current interest rate environment, standard models for pricing swaptions have to be extended to accommodate negative rates. In this thesis, we present the Free Boundary SABR and Mixture SABR models, introduced by Antonov et al. in 2015. They both rely on a free boundary, meaning interest rates can go indefinitely below zero, and with exact option pricing formulas available, they are promising alternatives for replacing the original SABR model. Here, we present the necessary theory, starting with some preliminary results on the CEV model. For the Free Boundary SABR, we present an approximate model for the case of non-zero correlation and correct the Monte Carlo scheme of the original article. In order to provide both an in-sample and out-of-sample analysis on market data, a large effort is devoted to the implementation procedure. The empirical findings on the Free Boundary SABR and the inability of the approximate non- zero correlation model to match market quotes leave us more sceptical than most other research available. Specifically, we disagree with the notion that the “stickiness” of interest rates is an attractive feature of the model. The Mixture SABR, on the other hand, performs well in general but for short expiries, and when insisting on an exact ATM fit, its performance deteriorates and is, on much of the available data, questionable

Vejleder: Rolf Poulsen
Censor:   Elisa Nicolato, Aarhus Universitet