The Impact of Computational Error on the Volatility Smile

41 Pages Posted: 4 Apr 2013

See all articles by Don M. Chance

Don M. Chance

Louisiana State University, Baton Rouge - Department of Finance; Louisiana State University, Baton Rouge - E.J. Ourso College of Business Administration

Thomas A. Hanson

Butler University - Lacy School of Business

Weiping Li

Civil Aviation Flight University of China ; Oklahoma State University

Jayaram Muthuswamy

Kent State University

Date Written: March 28, 2013

Abstract

It is well-known that the market prices of options produce implied volatilities that inexplicably vary by exercise price in a pattern often referred to as the volatility smile. This paper shows that not only do market prices produce volatility smiles, but so do model prices. This result occurs because of root finding algorithms, tolerance assumptions, numerical precisions, and quotation finiteness. Moreover, some assumptions result in patterns that resemble the smirks, and skews sometimes observed in market data. Consistent with empirical observations, the effects are greater the shorter the expiration. Elimination of these patterns is virtually impossible on a practical level, and even second-best results can be obtained only if options are traded with quadruple precision pricing and machine precision tolerance is assumed. We conclude that while alternative explanations for the smile can be true, prices generated under perfect conditions cannot even eliminate these smile, smirk, and skew patterns.

Keywords: Black-Scholes-Merton model, option pricing, implied volatility, volatility, volatility smile, computational finance, options

JEL Classification: C18, C63, G13

Suggested Citation

Chance, Don M. and Hanson, Thomas A. and Li, Weiping and Muthuswamy, Jayaram, The Impact of Computational Error on the Volatility Smile (March 28, 2013). Available at SSRN: https://ssrn.com/abstract=2243589 or http://dx.doi.org/10.2139/ssrn.2243589

Don M. Chance (Contact Author)

Louisiana State University, Baton Rouge - Department of Finance ( email )

2163 CEBA
Baton Rouge, LA 70803
United States

Louisiana State University, Baton Rouge - E.J. Ourso College of Business Administration

Baton Rouge, LA 70803-6308
United States
225-578-0372 (Phone)
225-578-6366 (Fax)

HOME PAGE: http://www.bus.lsu.edu/academics/finance/faculty/dchance/

Thomas A. Hanson

Butler University - Lacy School of Business ( email )

4600 Sunset Avenue
Indianapolis, IN 46208
United States

Weiping Li

Civil Aviation Flight University of China ( email )

46 Nanchang road
Guanghan, Sichuan 618307
China

Oklahoma State University ( email )

Stillwater, OK
United States

Jayaram Muthuswamy

Kent State University ( email )

Kent, OH 44242
United States

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