Deep Importance Sampling
Virrion, Benjamin (2020), Deep Importance Sampling. https://basepub.dauphine.fr/handle/123456789/21160
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02887331
Series titleCahier de recherche du CEREMADE
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We present a generic path-dependent importance sampling algorithm where the Girsanov induced change of probability on the path space is represented by a sequence of neural networks taking the past of the trajectory as an input. At each learning step, the neural networks' parameters are trained so as to reduce the variance of the Monte Carlo estimator induced by this change of measure. This allows for a generic path dependent change of measure which can be used to reduce the variance of any path-dependent financial payoff. We show in our numerical experiments that for payoffs consisting of either a call, an asymmetric combination of calls and puts, a symmetric combination of calls and puts, a multi coupon autocall or a single coupon autocall, we are able to reduce the variance of the Monte Carlo estimators by factors between 2 and 9. The numerical experiments also show that the method is very robust to changes in the parameter values, which means that in practice, the training can be done offline and only updated on a weekly basis.
Subjects / KeywordsPath-Dependence; Importance Sampling; Neural Networks
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Gajda, Dorota; Guihenneuc-Jouyaux, Chantal; Rousseau, Judith; Mengersen, Kerrie; Nur, Darfiana (2009) Communication / Conférence
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