Stochastic flow approach to Dupire's formula

B. Jourdain

doi:10.1007/s00780-007-0042-8

Stochastic flow approach to Dupire's formula

B. Jourdain

Research output: Contribution to journal › Article › peer-review

Abstract

The equivalent probabilistic formulation of Dupire's PDE is the put-call duality equality. In local volatility models including exponential Lévy jumps, we give a direct probabilistic proof for this result based on stochastic flow arguments. This approach also enables us to check the equivalent probabilistic formulation of various generalizations of Dupire's PDE recently obtained by Pironneau [C. R. Acad. Sci. Paris Ser. I 344(2) 127-133 (2007)] by the adjoint equation technique in the case of complex options.

Original language	English
Pages (from-to)	521-535
Number of pages	15
Journal	Finance and Stochastics
Volume	11
Issue number	4
DOIs	https://doi.org/10.1007/s00780-007-0042-8
Publication status	Published - 1 Jan 2007

Keywords

Dupire's PDE
Put-call duality
Stochastic flows
Stock models with jumps and local volatility

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10.1007/s00780-007-0042-8

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KW - Put-call duality

KW - Stochastic flows

KW - Stock models with jumps and local volatility

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Stochastic flow approach to Dupire's formula

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Keywords

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