Calculating Delta Greeks of Callable Exotics in the LMM: A New Approach

Abstract

In this research note, we present a new method to calculate delta greeks of callable exotics in the context of LIBOR Market Model. LIBOR market models are very popular for pricing and risk management of interest rate exotics but calculation of sensitivities with these models is usually not straightforward and can be very time consuming. We show that it is possible to calculate delta greeks by new alternative method which is quite accurate and calculates all greeks in a single simulation just like pathwise methods but is simpler in nature. Our approach is a regression method to calculate the sensitivities of these exotics. Though regression is used very widely to calculate sensitivities or betas in empirical finance, almost no one uses them to calculate sensitivities in high dimensional simulation models like LIBOR Market Model. We show with different examples that this could be an efficient and accurate method to calculate delta greeks for a wide variety of callable interest rate exotic instruments. The method should be attractive since it is very easy to program and can have almost the same exactness as the pathwise greeks methods for a wide variety of structures.

Keywords: Delta Greeks, Sensitivities, Callable LIBOR exotics, LMM, LIBOR Market Model, Regression methods

JEL Classification: C15,G12,G13