Mixing Monte-Carlo and Partial Differential Equations for Pricing Options

Tobias Lipp, G Loeper, Olivier Pironneau

Research output: Chapter in Book/Report/Conference proceedingChapter (Report)Researchpeer-review

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.
Original languageEnglish
Title of host publicationPartial Differential Equations
Subtitle of host publicationTheory, Control and Approximation
EditorsPhilippe G Ciarlet, Tatsien Li, Yvon Maday
Place of PublicationHeidelberg Germany
PublisherSpringer-Verlag London Ltd.
Pages323-347
Number of pages25
ISBN (Electronic)9783642414015
ISBN (Print)9783642414008
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Monte-Carlo
  • Partial differential equations
  • Heston model
  • Financial mathematics
  • Option pricing

Cite this

Lipp, T., Loeper, G., & Pironneau, O. (2014). Mixing Monte-Carlo and Partial Differential Equations for Pricing Options. In P. G. Ciarlet, T. Li, & Y. Maday (Eds.), Partial Differential Equations: Theory, Control and Approximation (pp. 323-347). Heidelberg Germany: Springer-Verlag London Ltd.. https://doi.org/10.1007/978-3-642-41401-5_13
Lipp, Tobias ; Loeper, G ; Pironneau, Olivier. / Mixing Monte-Carlo and Partial Differential Equations for Pricing Options. Partial Differential Equations: Theory, Control and Approximation. editor / Philippe G Ciarlet ; Tatsien Li ; Yvon Maday. Heidelberg Germany : Springer-Verlag London Ltd., 2014. pp. 323-347
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Lipp, T, Loeper, G & Pironneau, O 2014, Mixing Monte-Carlo and Partial Differential Equations for Pricing Options. in PG Ciarlet, T Li & Y Maday (eds), Partial Differential Equations: Theory, Control and Approximation. Springer-Verlag London Ltd., Heidelberg Germany, pp. 323-347. https://doi.org/10.1007/978-3-642-41401-5_13

Mixing Monte-Carlo and Partial Differential Equations for Pricing Options. / Lipp, Tobias; Loeper, G; Pironneau, Olivier.

Partial Differential Equations: Theory, Control and Approximation. ed. / Philippe G Ciarlet; Tatsien Li; Yvon Maday. Heidelberg Germany : Springer-Verlag London Ltd., 2014. p. 323-347.

Research output: Chapter in Book/Report/Conference proceedingChapter (Report)Researchpeer-review

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AU - Pironneau, Olivier

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N2 - 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.

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KW - Partial differential equations

KW - Heston model

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KW - Option pricing

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Lipp T, Loeper G, Pironneau O. Mixing Monte-Carlo and Partial Differential Equations for Pricing Options. In Ciarlet PG, Li T, Maday Y, editors, Partial Differential Equations: Theory, Control and Approximation. Heidelberg Germany: Springer-Verlag London Ltd. 2014. p. 323-347 https://doi.org/10.1007/978-3-642-41401-5_13