THE EFFICIENT COMPUTATION OF PRICES AND GREEKS FOR CALLABLE RANGE ACCRUALS USING THE DISPLACED-DIFFUSION LMM

Abstract

We study the simulation of range accrual coupons when valuing callable range accruals in the displaced-diffusion LIBOR market model (DDLMM). We introduce a number of new improvements that lead to significant efficiency improvements, and explain how to apply the adjoint-improved pathwise method to calculate deltas and vegas under the new improvements, which was not previously possible for callable range accruals. One new improvement is based on using a Brownian-bridge-type approach for simulating the range accrual coupons. We consider a variety of examples, including when the reference rate is a LIBOR rate, when it is a spread between swap rates, and when the multiplier for the range accrual coupon is stochastic.