Moment Approximations of Displaced Forward-LIBOR Rates with Application to Swaptions

26 Pages Posted: 1 Jun 2020

See all articles by Jacques van Appel

Jacques van Appel

University of Johannesburg

Thomas McWalter

University of Cape Town (UCT); University of Johannesburg

Date Written: May 2, 2020

Abstract

We present an algorithm to approximate moments for forward rates under a displaced lognormal forward-LIBOR model (DLFM). Since the joint distribution of rates is unknown, we use a multi-dimensional full weak order 2.0 Ito-Taylor expansion in combination with a second-order Delta method. This more accurately accounts for state dependence in the drift terms, improving upon previous approaches. To verify this improvement we conduct quasi-Monte Carlo simulations. We use the new mean approximation to provide an improved swaption volatility approximation, and compare this to the approaches of Rebonato, Hull-White and Kawai, adapted to price swaptions under the DLFM. Rebonato and Hull-White are found to be the least accurate. While Kawai is the most accurate, it is computationally inefficient. Numerical results show that our approach strikes a balance between accuracy and efficiency.

Keywords: Displaced LIBOR Model, Moments, Swaption, Volatility Approximation

JEL Classification: G12, G13, C51

Suggested Citation

van Appel, Jacques and McWalter, Thomas, Moment Approximations of Displaced Forward-LIBOR Rates with Application to Swaptions (May 2, 2020). Available at SSRN: https://ssrn.com/abstract=3591458 or http://dx.doi.org/10.2139/ssrn.3591458

Jacques Van Appel

University of Johannesburg ( email )

PO Box 524
Auckland Park
Johannesburg, Gauteng 2006
South Africa

Thomas McWalter (Contact Author)

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

University of Johannesburg ( email )

PO Box 524
Auckland Park
Johannesburg, Gauteng 2006
South Africa

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