Reconstruction of Volatility: Pricing Index Options by the Steepest Descent Approximation

Courant Institute-NYU Working Paper

18 Pages Posted: 21 Nov 2002

See all articles by Marco Avellaneda

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Dash Boyer-Olson

Gargoyle Strategic Investments L.L.C.

Date Written: June 15, 2002

Abstract

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

Avellaneda, Marco and Boyer-Olson, Dash, Reconstruction of Volatility: Pricing Index Options by the Steepest Descent Approximation (June 15, 2002). Courant Institute-NYU Working Paper, Available at SSRN: https://ssrn.com/abstract=316399 or http://dx.doi.org/10.2139/ssrn.316399

Marco Avellaneda (Contact Author)

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

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Dash Boyer-Olson

Gargoyle Strategic Investments L.L.C. ( email )

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Philadelphia, PA 19103
United States

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