An exact and efficient method for computing cross-Gammas of Bermudan swaptions and cancelable swaps under the Libor market model

Mark S. Joshi, Dan Zhu

Research output: Contribution to journalArticleResearchpeer-review


We introduce a new simulation algorithm for computing the Hessians of Bermudan swaptions and cancelable swaps. The resulting pathwise estimates are unbiased and accurate. Given the exercise strategy, the pathwise angularities are removed by a sequence of measure changes.The change of measure at each exercise time is chosen to be optimal in terms of minimizing the variance of the likelihood ratio terms. Numerical results for the Hessian of cancelable swaps are presented to demonstrate the speed and efficacy of the method.

Original languageEnglish
Pages (from-to)113-137
Number of pages25
JournalJournal of Computational Finance
Issue number1
Publication statusPublished - 1 Sep 2016
Externally publishedYes


  • Bermudan products
  • Exercise strategy
  • Hessian
  • Measure changes
  • Monte Carlo simulation

Cite this