[Méthodes de grandes déviations et pricing d'options sur indice]
Nous montrons une formule asymptotique donnant la volatilité implicite d'une option sur indice à partir des volatilités des actifs sous-jacents. La démonstration repose sur les estimations de densités de diffusion en temps petit du type grandes déviation de Varadhan (Comm. Pure Appl. Math. 20 (1967)). On pourra trouver une version détaillée de ces résultats dans l'article (RISK 15 (10) (2002)).
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)).
Accepté le :
Publié le :
Marco Avellaneda 1 ; Dash Boyer-Olson 1 ; Jérôme Busca 2 ; Peter Friz 1
@article{CRMATH_2003__336_3_263_0,
author = {Marco Avellaneda and Dash Boyer-Olson and J\'er\^ome Busca and Peter Friz},
title = {Application of large deviation methods to the pricing of index options in finance},
journal = {Comptes Rendus. Math\'ematique},
pages = {263--266},
publisher = {Elsevier},
volume = {336},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00032-3},
language = {en},
}
TY - JOUR AU - Marco Avellaneda AU - Dash Boyer-Olson AU - Jérôme Busca AU - Peter Friz TI - Application of large deviation methods to the pricing of index options in finance JO - Comptes Rendus. Mathématique PY - 2003 SP - 263 EP - 266 VL - 336 IS - 3 PB - Elsevier DO - 10.1016/S1631-073X(03)00032-3 LA - en ID - CRMATH_2003__336_3_263_0 ER -
%0 Journal Article %A Marco Avellaneda %A Dash Boyer-Olson %A Jérôme Busca %A Peter Friz %T Application of large deviation methods to the pricing of index options in finance %J Comptes Rendus. Mathématique %D 2003 %P 263-266 %V 336 %N 3 %I Elsevier %R 10.1016/S1631-073X(03)00032-3 %G en %F CRMATH_2003__336_3_263_0
Marco Avellaneda; Dash Boyer-Olson; Jérôme Busca; Peter Friz. Application of large deviation methods to the pricing of index options in finance. Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 263-266. doi : 10.1016/S1631-073X(03)00032-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00032-3/
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