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Mixing Monte-Carlo and Partial Differential Equations for Pricing Options

  • Tobias Lipp
  • Grégoire Loeper
  • Olivier Pironneau

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 

Mathematics Subject Classification

91B28 65L60 82B31 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Tobias Lipp
    • 1
  • Grégoire Loeper
    • 2
  • Olivier Pironneau
    • 1
  1. 1.LJLL-UPMCParis cedex 5France
  2. 2.BNP-ParibasParisFrance

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