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

ASJC Scopus subject areas

  • Mathematics(all)

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