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

Fingerprint

Finance
Large Deviations
Pricing
Implied Volatility
Steepest Descent
Probability Distribution Function
Stock Prices
Correlation Matrix
Multivariate Distribution
Asymptotic Formula
Volatility
Diffusion Process
Skew
Approximation
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Application of large deviation methods to the pricing of index options in finance. / Avellaneda, Marco; Boyer-Olson, Dash; Busca, Jérôme; Friz, Peter.

In: Comptes Rendus Mathematique, Vol. 336, No. 3, 01.02.2003, p. 263-266.

Research output: Contribution to journalArticle

Avellaneda, Marco ; Boyer-Olson, Dash ; Busca, Jérôme ; Friz, Peter. / Application of large deviation methods to the pricing of index options in finance. In: Comptes Rendus Mathematique. 2003 ; Vol. 336, No. 3. pp. 263-266.
@article{9b38e4cfdac94077b474eca91da261fc,
title = "Application of large deviation methods to the pricing of index options in finance",
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)).",
author = "Marco Avellaneda and Dash Boyer-Olson and J{\'e}r{\^o}me Busca and Peter Friz",
year = "2003",
month = "2",
day = "1",
doi = "10.1016/S1631-073X(03)00032-3",
language = "English (US)",
volume = "336",
pages = "263--266",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier Masson",
number = "3",

}

TY - JOUR

T1 - Application of large deviation methods to the pricing of index options in finance

AU - Avellaneda, Marco

AU - Boyer-Olson, Dash

AU - Busca, Jérôme

AU - Friz, Peter

PY - 2003/2/1

Y1 - 2003/2/1

N2 - 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)).

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)).

UR - http://www.scopus.com/inward/record.url?scp=0037715212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037715212&partnerID=8YFLogxK

U2 - 10.1016/S1631-073X(03)00032-3

DO - 10.1016/S1631-073X(03)00032-3

M3 - Article

AN - SCOPUS:0037715212

VL - 336

SP - 263

EP - 266

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 3

ER -