Application of large deviation methods to the pricing of index options in finance

Marco Avellaneda; Dash Boyer-Olson; Jérôme Busca; Peter Friz

doi:10.1016/S1631-073X(03)00032-3

Application of large deviation methods to the pricing of index options in finance

Marco Avellaneda, Dash Boyer-Olson, Jérôme Busca, Peter Friz

Mathematics

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

Abstract

We develop an asymptotic formula for calculating the implied volatility of European index options based on the volatility skews of the options on the underlying stocks and on a given correlation matrix for the basket. The derivation uses the steepest-descent approximation for evaluating the multivariate probability distribution function for stock prices, which is based on large-deviation estimates of diffusion processes densities by Varadhan (Comm. Pure Appl. Math. 20 (1967)). A detailed version of these results can be found in (RISK 15 (10) (2002)).

Original language	English (US)
Pages (from-to)	263-266
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	336
Issue number	3
DOIs	https://doi.org/10.1016/S1631-073X(03)00032-3
State	Published - Feb 1 2003

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Mathematics(all)

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AB - We develop an asymptotic formula for calculating the implied volatility of European index options based on the volatility skews of the options on the underlying stocks and on a given correlation matrix for the basket. The derivation uses the steepest-descent approximation for evaluating the multivariate probability distribution function for stock prices, which is based on large-deviation estimates of diffusion processes densities by Varadhan (Comm. Pure Appl. Math. 20 (1967)). A detailed version of these results can be found in (RISK 15 (10) (2002)).

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Application of large deviation methods to the pricing of index options in finance

Abstract

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