Modeling and Estimating Volatility of Options on Standard & Poor's 500 Index

21 Pages Posted: 1 Apr 2013

See all articles by Boleslaw Borkowski

Boleslaw Borkowski

Warsaw University of Life Sciences, Department of Econometrics and Statistics

Monika Krawiec

Warsaw University of Life Sciences, Department of Econometrics and Statistics

Yochanan Shachmurove

City University of New York, CUNY City College of New York - Department of Economics; The University of Pennsylvania - Department of Economics

Date Written: February 1, 2013

Abstract

This paper explores the impact of volatility estimation methods on theoretical option values based upon the Black-Scholes-Merton (BSM) model. Volatility is the only input used in the BSM model that cannot be observed in the market or a priori determined in a contract. Thus, properly calculating volatility is crucial. Two approaches to estimate volatility are implied volatility and historical prices. Iterative techniques are applied, based on daily S&P index options. Additionally, using option data on S&P 500 Index listed on the Chicago Board of Options Exchange, historical volatility can be estimated.

Keywords: historical volatility; option premium; index options; Black-Scholes-Merton model; Chicago Board of Options Exchange

JEL Classification: C0, C01, C2, C58, D53, G0, G13, G17

Suggested Citation

Borkowski, Boleslaw and Krawiec, Monika and Shachmurove, Yochanan, Modeling and Estimating Volatility of Options on Standard & Poor's 500 Index (February 1, 2013). PIER Working Paper No. 13-015, Available at SSRN: https://ssrn.com/abstract=2242934 or http://dx.doi.org/10.2139/ssrn.2242934

Boleslaw Borkowski

Warsaw University of Life Sciences, Department of Econometrics and Statistics ( email )

ul. Nowoursynowska 159
Warsaw, 02-776
Poland

Monika Krawiec

Warsaw University of Life Sciences, Department of Econometrics and Statistics ( email )

ul. Nowoursynowska 159
Warsaw, 02-776
Poland

Yochanan Shachmurove (Contact Author)

City University of New York, CUNY City College of New York - Department of Economics ( email )

160 Convent Avenue
New York, NY 10031
United States
212-650-6202 (Phone)

The University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-1090 (Phone)
215-573-2057 (Fax)

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