TY - JOUR
T1 - Rolling Adjoints
T2 - Fast Greeks along Monte Carlo scenarios for early-exercise options
AU - Jain, Shashi
AU - Leitao, Álvaro
AU - Oosterlee, Cornelis W.
N1 - Funding Information:
Currently, I am a BGSMath-María de Maeztu JUNIOR postdoctoral researcher in the Riskcenter-IREA research group at the University of Barcelona, funded by the Barcelona Graduate School of Mathematics after competitive call. I have obtained my B.Sc. degree in Computer Science at the University of A Coruña. After that, I got an M.Sc. in Mathematical Engineering at the University of Vigo with specialization in numerical techniques for mathematical finance. Then, I have worked at the Department of Mathematics in University of A Coruña on the high-performance implementation of mathematical models with financial applications. In 2013, I moved to The Netherlands to start my doctoral education awarded by a Marie Curie fellowship, in the framework of an International Training Network (ITN) called STRIKE – Novel Methods in Computational Finance. I carried out my doctoral studies at the Delft Institute of Applied Mathematics (DIAM) in the Delft University of Technology (TU Delft) and the Scientific Computing (SC) research group of the Centrum Wiskunde & Informatica (CWI), the National research center in mathematics and computer science in Amsterdam. My research topic is focused on the development of efficient numerical solution techniques in financial mathematics, a discipline that lies at the intersection of numerical analysis and stochastic calculus. My expertise includes stochastic processes and stochastic differential equations (SDEs), Monte Carlo methods and Fourier inversion techniques, applied to problems appearing in the financial sector. Particularly, I am interested in hybrid solutions for advanced quantitative problems, combining several methodologies (including computation) aiming a satisfactory balance between precision, robustness and efficiency. My expertise also includes GPU parallel computing. Regarding my programming skills, I regularly use C, Python and Matlab. I have taught several courses on Python programming for financial applications.
Funding Information:
Álvaro Leitao acknowledges financial support from the Spanish Ministry of Science and Innovation, through the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445).
Publisher Copyright:
© 2019
PY - 2019/4
Y1 - 2019/4
N2 - 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.
AB - 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.
KW - Early-exercise
KW - Greeks
KW - Monte Carlo
KW - Sensitivities along paths
KW - SGBM
UR - http://www.scopus.com/inward/record.url?scp=85065248100&partnerID=8YFLogxK
U2 - 10.1016/j.jocs.2019.03.001
DO - 10.1016/j.jocs.2019.03.001
M3 - Article
AN - SCOPUS:85065248100
SN - 1877-7503
VL - 33
SP - 95
EP - 112
JO - Journal of Computational Science
JF - Journal of Computational Science
ER -