It is possible to price CRAs using the LMM using a Brownian bridge technique. You simulate
to each coupon date and then infer the expectation of the coupon given the values of
the rates at the start and end of the accrual period.
http://ssrn.com/abstract=1461285
Interpolation Schemes in the Displaced-Diffusion LIBOR Market Model and the Efficient Pricing and Greeks for Callable Range Accruals
Christopher Beveridge
University of Melbourne - Centre for Actuarial Studies
Mark S. Joshi
University of Melbourne - Centre for Actuarial Studies
August 25, 2009
Abstract:
We introduce a new arbitrage-free interpolation scheme for the displaced-diffusion LIBOR market model. Using this new extension, and the Piterbarg interpolation scheme, we study the simulation of range accrual coupons when valuing callable range accruals in the displaced-diffusion LIBOR market model. 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 to 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.