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Mixing Monte-Carlo and Partial Differential Equations for Pricing Options

In: Partial Differential Equations: Theory, Control and Approximation

Author

Listed:
  • Tobias Lipp

    (LJLL-UPMC)

  • Grégoire Loeper

    (BNP-Paribas)

  • Olivier Pironneau

    (LJLL-UPMC)

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.

Suggested Citation

  • Tobias Lipp & Grégoire Loeper & Olivier Pironneau, 2014. "Mixing Monte-Carlo and Partial Differential Equations for Pricing Options," Springer Books, in: Philippe G. Ciarlet & Tatsien Li & Yvon Maday (ed.), Partial Differential Equations: Theory, Control and Approximation, edition 127, pages 323-347, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-41401-5_13
    DOI: 10.1007/978-3-642-41401-5_13
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