Rolling Adjoints

Fast Greeks along Monte Carlo scenarios for early-exercise options

Journal article (2019)

Authors

S. Jain Indian Institute of Science
A. Leitao Rodriguez Universitat Politecnica de Catalunya, Barcelona Graduate School of Mathematics
C.W. Oosterlee Numerical Analysis - EEMCS , Centrum Wiskunde & Informatica (CWI)
Research Group
Numerical Analysis (EEMCS) (TU Delft)
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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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.

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