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) |
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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)