Reconstruction of Volatility: Pricing Index Options by the Steepest Descent Approximation
Courant Institute-NYU Working Paper
18 Pages Posted: 21 Nov 2002
Date Written: June 15, 2002
We propose a formula for calculating the implied volatility of 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 the multivariate probability distribution function of forward prices. A simple financial justification is provided. We apply the formula to compute the implied volatilities of liquidly-traded options on exchange-traded funds (ETF) across different strikes. Our theoretical results were found to be in good agreement with contemporaneous quotes on the Chicago Board of Options Exchange (CBOE) and the American Stock Exchange (AMEX).
JEL Classification: C0, C3, G13
Suggested Citation: Suggested Citation