Mispricing in the Black-Scholes model: an exploratory analysis

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1993
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Sriplung, Kai-one
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Stanley R. Johnson
Wayne A. Fuller
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Economics

The Department of Economic Science was founded in 1898 to teach economic theory as a truth of industrial life, and was very much concerned with applying economics to business and industry, particularly agriculture. Between 1910 and 1967 it showed the growing influence of other social studies, such as sociology, history, and political science. Today it encompasses the majors of Agricultural Business (preparing for agricultural finance and management), Business Economics, and Economics (for advanced studies in business or economics or for careers in financing, management, insurance, etc).

History
The Department of Economic Science was founded in 1898 under the Division of Industrial Science (later College of Liberal Arts and Sciences); it became co-directed by the Division of Agriculture in 1919. In 1910 it became the Department of Economics and Political Science. In 1913 it became the Department of Applied Economics and Social Science; in 1924 it became the Department of Economics, History, and Sociology; in 1931 it became the Department of Economics and Sociology. In 1967 it became the Department of Economics, and in 2007 it became co-directed by the Colleges of Agriculture and Life Sciences, Liberal Arts and Sciences, and Business.

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1898–present

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  • Department of Economic Science (1898–1910)
  • Department of Economics and Political Science (1910-1913)
  • Department of Applied Economics and Social Science (1913–1924)
  • Department of Economics, History and Sociology (1924–1931)
  • Department of Economics and Sociology (1931–1967)

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Abstract

The Black-Scholes option pricing model has been highly influential in security trading and in analyses of risk-price relationships, despite the fact that it has been shown to have an apparent unexplainable mispricing bias. This study examines the mispricing exhibited by the Black-Scholes model and shows that it can be explained by the estimation procedures utilized and the measures of volatility. Specifically, a model is constructed to test for the systematic over- or underpricing of the Black-Scholes model. Striking price and time-to-maturity are included in the model. The model also includes an autoregressive error structure. Recognizing the autocorrelation in the errors improves estimation efficiency and predictability of future option prices. The method of entering implied volatility into the model has a great impact. When only one estimated implied volatility was used to explain the option data, the Black-Scholes model exhibited a bias that was a similar function of striking price for all of the securities studied. When separate estimated implied volatilities for different option positions were used, the bias as a function of striking price and time-to-maturity varied among securities. Predictions of market option prices based on the model containing striking price, time-to-maturity, and an autoregressive error structure were more accurate than those based on the Black-Scholes model.

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Fri Jan 01 00:00:00 UTC 1993