Expansion formulas for european options in a local volatility model

E. Benhamou; E. Gobet; M. Miri

doi:10.1142/S0219024910005887

Expansion formulas for european options in a local volatility model

E. Benhamou
, E. Gobet
, M. Miri

Pricing Partners
LTHE (UMR 5564 CNRS/IRD/Université de Grenoble)

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

Abstract

Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms.

Original language	English
Pages (from-to)	603-634
Number of pages	32
Journal	International Journal of Theoretical and Applied Finance
Volume	13
Issue number	4
DOIs	https://doi.org/10.1142/S0219024910005887
Publication status	Published - 1 Jan 2010
Externally published	Yes

Keywords

CEV model
European options
Local volatility model
Malliavin calculus
asymptotic expansion
small diffusion process

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10.1142/S0219024910005887

Cite this

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title = "Expansion formulas for european options in a local volatility model",

abstract = "Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms.",

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AU - Benhamou, E.

AU - Gobet, E.

AU - Miri, M.

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N2 - Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms.

AB - Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms.

KW - CEV model

KW - European options

KW - Local volatility model

KW - Malliavin calculus

KW - asymptotic expansion

KW - small diffusion process

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DO - 10.1142/S0219024910005887

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EP - 634

JO - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

IS - 4

ER -

Expansion formulas for european options in a local volatility model

Abstract

Keywords

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