Mixing Monte-Carlo and partial differential equations for pricing options

Tobias Lipp, Gregoire Loeper, Olivier Pironneau

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

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
Pages (from-to)255-276
Number of pages22
JournalChinese Annals of Mathematics. Series B
Volume34
Issue number2
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

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

Cite this

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Mixing Monte-Carlo and partial differential equations for pricing options. / Lipp, Tobias; Loeper, Gregoire; Pironneau, Olivier.

In: Chinese Annals of Mathematics. Series B, Vol. 34, No. 2, 2013, p. 255-276.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Mixing Monte-Carlo and partial differential equations for pricing options

AU - Lipp, Tobias

AU - Loeper, Gregoire

AU - Pironneau, Olivier

PY - 2013

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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.

AB - 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.

KW - Financial mathematics

KW - Heston model

KW - Monte-Carlo

KW - Option pricing

KW - Partial differential equations

UR - http://link.springer.com/content/pdf/10.1007%2Fs11401-013-0763-2.pdf

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DO - 10.1007/s11401-013-0763-2

M3 - Article

VL - 34

SP - 255

EP - 276

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

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