Interpolation Schemes in the Displaced-Diffusion LIBOR Market Model and the Efficient Pricing and Greeks for Callable Range Accruals

46 Pages Posted: 26 Aug 2009 Last revised: 27 Feb 2010

Christopher Beveridge

University of Melbourne - Centre for Actuarial Studies

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies

Date Written: 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.

Keywords: LIBOR market model, BGM, range accrual, interpolation scheme, Monte Carlo, early exercise, Greeks, pathwise method, delta, vega

JEL Classification: C19, G13

Suggested Citation

Beveridge, Christopher and Joshi, Mark S., Interpolation Schemes in the Displaced-Diffusion LIBOR Market Model and the Efficient Pricing and Greeks for Callable Range Accruals (August 25, 2009). Available at SSRN: https://ssrn.com/abstract=1461285 or http://dx.doi.org/10.2139/ssrn.1461285

Christopher Beveridge (Contact Author)

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

Mark Joshi

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

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