Accounting for Biases in Black-Scholes

46 Pages Posted: 3 Sep 2004

See all articles by David K. Backus

David K. Backus

NYU Stern School of Business; National Bureau of Economic Research (NBER)

Silverio Foresi

Goldman Sachs Group, Inc. - Quantitative Strategy Group

Liuren Wu

City University of New York, CUNY Baruch College - Zicklin School of Business

Date Written: August 31, 2004

Abstract

Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of at-the-money options increases, on average, with maturity). We account for both using Gram-Charlier expansions to approximate the conditional distribution of the logarithm of the price of the underlying security. In this setting, volatility is approximately a quadratic function of moneyness, a result we use to infer skewness and kurtosis from volatility smiles. Evidence suggests that both kurtosis in currency prices and biases in Black-Scholes option prices decline with maturity.

Keywords: Currency options, skewness and kurtosis, Gram-Charlier expansions, implied volatility

JEL Classification: G12, G13, F31, C14

Suggested Citation

Backus, David K. and Foresi, Silverio and Wu, Liuren, Accounting for Biases in Black-Scholes (August 31, 2004). Available at SSRN: https://ssrn.com/abstract=585623 or http://dx.doi.org/10.2139/ssrn.585623

David K. Backus

NYU Stern School of Business

44 West Fourth Street
New York, NY 10012
United States
212-998-0873 (Phone)
212-995-4220 (Fax)

HOME PAGE: http://pages.stern.nyu.edu/~dbackus/

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

HOME PAGE: http://pages.stern.nyu.edu/~dbackus/

Silverio Foresi

Goldman Sachs Group, Inc. - Quantitative Strategy Group ( email )

32 Old Slip, 24th Floor
New York, NY 10005
United States
(212) 357-3508 (Phone)

Liuren Wu (Contact Author)

City University of New York, CUNY Baruch College - Zicklin School of Business ( email )

One Bernard Baruch Way
Box B10-247
New York, NY 10010
United States
646-312-3509 (Phone)
646-312-3451 (Fax)

HOME PAGE: http://faculty.baruch.cuny.edu/lwu/

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
1,361
Abstract Views
4,692
rank
14,228
PlumX Metrics