Moment Approximations of Displaced Forward-LIBOR Rates with Application to Swaptions
26 Pages Posted: 1 Jun 2020
Date Written: May 2, 2020
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
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