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 | |
| State | Published - Feb 1 2003 |
ASJC Scopus subject areas
- Mathematics(all)
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Avellaneda, M., Boyer-Olson, D., Busca, J., & Friz, P. (2003). Application of large deviation methods to the pricing of index options in finance. Comptes Rendus Mathematique, 336(3), 263-266. https://doi.org/10.1016/S1631-073X(03)00032-3