Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options

Shashi Jain, Álvaro Leitao, Cornelis W. Oosterlee

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper we extend the Stochastic Grid Bundling Method (SGBM), a regress-later Monte Carlo scheme for pricing early-exercise options, with an adjoint method to compute in a highly efficient manner the option sensitivities (the “Greeks”)along the Monte Carlo paths, with reasonable accuracy. The path-wise SGBM Greeks computation is based on the conventional path-wise sensitivity analysis, however, for a regress-later technique. The resulting sensitivities at the end of the monitoring period are implicitly rolled over into the sensitivities of the regression coefficients of the previous monitoring date. For this reason, we name the method Rolling Adjoints, which facilitates Smoking Adjoints [M. Giles, P. Glasserman, Smoking adjoints: fast Monte Carlo Greeks, Risk 19 (1)(2006)88–92]to compute conditional sensitivities along the paths for options with early-exercise features.

Original languageEnglish
Pages (from-to)95-112
Number of pages18
JournalJournal of Computational Science
Volume33
DOIs
Publication statusPublished - 2019

Keywords

  • Early-exercise
  • Greeks
  • Monte Carlo
  • Sensitivities along paths
  • SGBM

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