Concurrence Between the Displaced Libor Market and Hull-White Models

Thantsha, Kgothatso

Concurrence Between the Displaced Libor Market and Hull-White Models

Master Thesis

2021

Abstract

The concurrence between the displaced lognormal forward-Libor model (DLFM), Gaussian Heath-Jarrow-Morton (GHJM) model and Hull-White (HW) model is explored. We briefly present the theory underpinning these models, specifically focusing on single factors. A useful volatility relation result adapted from Andersen and Piterbarg (2010) is derived. It relates the instantaneous volatility functions of the GHJM model and the DLFM model. The volatility relation allows us to state a specific GHJM model and derive a corresponding DLFM model that it is concurrent with. We take the Hull-White model and derive its corresponding GHJM model, the volatility of the GHJM model is then fed into the volatility relation in order to derive the corresponding DLFM model. This was sufficient mathematical proof of the concurrence, but numerical confirmation is also essential. The HW, GHJM and DLFM models were implemented, with applications to pricing European swaptions. Numerical results show that swaption prices are consistent across the three models. This provides good numerical evidence to support the concurrence between the DLFM and HW models.

Keywords

Mathematical Finance

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