Mixing Monte-Carlo and Partial Differential Equations for Pricing Options

Tobias Lipp, Grégoire Loeper and Olivier Pironneau
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Tobias Lipp: LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Grégoire Loeper: Monash University [Clayton]
Olivier Pironneau: LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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Abstract: There is a need for very fast option pricers when the financial objects are mod-eled by complex systems of stochastic differential equations. Here the authors investigate option pricers based on mixed Monte-Carlo partial differential solvers for stochastic volatility models such as Heston's. It is found that orders of magnitude in speed are gained on full Monte-Carlo algorithms by solving all equations but one by a Monte-Carlo method, and pricing the underlying asset by a partial differential equation with random coefficients, derived by Itô calculus. This strategy is investigated for vanilla options, barrier options and American options with stochastic volatilities and jumps optionally.

Keywords: Option pricing; mathematics; Financial; Monte-Carlo; Partial differential equations; Heston model (search for similar items in EconPapers)
Date: 2013
Note: View the original document on HAL open archive server: https://hal.sorbonne-universite.fr/hal-01558826
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Citations: View citations in EconPapers (3)

Published in Chinese Annals of Mathematics - Series B, 2013, 34 (B2), pp.255 - 276. ⟨10.1007/s11401-013-0763-2⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01558826

DOI: 10.1007/s11401-013-0763-2

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