Mixing Monte-Carlo and Partial Differential Equations for Pricing Options

Tobias Lipp (), Grégoire Loeper () and Olivier Pironneau ()
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Tobias Lipp: LJLL-UPMC
Grégoire Loeper: BNP-Paribas
Olivier Pironneau: LJLL-UPMC

A chapter in Partial Differential Equations: Theory, Control and Approximation, 2014, pp 323-347 from Springer

Abstract: Abstract There is a need for very fast option pricers when the financial objects are modeled 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: Monte-Carlo; Partial differential equations; Heston model; Financial mathematics; Option pricing; 91B28; 65L60; 82B31 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-41401-5_13

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DOI: 10.1007/978-3-642-41401-5_13

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