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Accelerating Pathwise Greeks In The Libor Market Model

Author

Listed:
  • MARK JOSHI

    (Centre for Actuarial Studies, University of Melbourne, VIC3010, Australia)

  • ALEXANDER WIGUNA

    (Deutsche Bank AG, One Raffles Quay #18-00, South Tower, Singapore 048583, Singapore)

Abstract

In the framework of the displaced-diffusion LIBOR market model, we derive the pathwise adjoint method for the iterative predictor-corrector and one of the 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, used, 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.

Suggested Citation

  • Mark Joshi & Alexander Wiguna, 2012. "Accelerating Pathwise Greeks In The Libor Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-33.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:02:n:s0219024912500124
    DOI: 10.1142/S0219024912500124
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