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Mixing Monte-Carlo and Partial Differential Equations for Pricing Options: In honor of the scientific heritage of Jacques-Louis Lions

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.
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Tobias Lipp, Grégoire Loeper, Olivier Pironneau. Mixing Monte-Carlo and Partial Differential Equations for Pricing Options: In honor of the scientific heritage of Jacques-Louis Lions. Chinese Annals of Mathematics - Series B, Springer Verlag, 2013, 34 (B2), pp.255 - 276. ⟨10.1007/s11401-013-0763-2⟩. ⟨hal-01558826⟩

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