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

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)263-266
Number of pages4
JournalComptes Rendus Mathematique
Volume336
Issue number3
DOIs
StatePublished - Feb 1 2003

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ASJC Scopus subject areas

  • Mathematics(all)

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