Accelerating Pathwise Greeks in the LIBOR Market Model

28 Pages Posted: 25 Feb 2011 Last revised: 1 Aug 2011

See all articles by Mark S. Joshi

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies (deceased)

Alexander Wiguna

affiliation not provided to SSRN

Date Written: February 24, 2011

Abstract

In the framework of the displaced-diffusion LIBOR market model, we derive the pathwise adjoint method for the iterative predictor-corrector and Glasserman-Zhao drift approximations in the spot measure. This allows us to compute fast deltas and vegas under these schemes. We compare the discretisation bias obtained when computing Greeks with these methods to those obtained under the log-Euler and predictor-corrector approximations by performing tests with interest rate caplets and cancellable receiver swaps. The two predictor-corrector type methods were the most accurate by far. In particular, we found the iterative predictor-corrector method to be more accurate and slightly faster than the predictor-corrector method, the Glasserman-Zhao method to be relatively fast but highly inconsistent, and the log-Euler method to be reasonably accurate but only at low volatilities. Standard errors were not significantly different across all four discretisations.

Keywords: LIBOR market model, pathwise Greeks, adjoint methods

JEL Classification: G13

Suggested Citation

Joshi, Mark and Wiguna, Alexander, Accelerating Pathwise Greeks in the LIBOR Market Model (February 24, 2011). Available at SSRN: https://ssrn.com/abstract=1768409 or http://dx.doi.org/10.2139/ssrn.1768409

Mark Joshi (Contact Author)

University of Melbourne - Centre for Actuarial Studies (deceased) ( email )

Melbourne, 3010
Australia

Alexander Wiguna

affiliation not provided to SSRN ( email )

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