On the Number of State Variables in Options Pricing

On the Number of State Variables in Options Pricing

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Article ID: iaor20108803
Volume: 56
Issue: 11
Start Page Number: 2058
End Page Number: 2075
Publication Date: Nov 2010
Journal: Management Science
Authors: ,
Keywords: option pricing, principal component analysis
Abstract:

In this paper, we investigate the methodological issue of determining the number of state variables required for options pricing. After showing the inadequacy of the principal component analysis approach, which is commonly used in the literature, we adopt a nonparametric regression technique with nonlinear principal components extracted from the implied volatilities of various moneyness and maturities as proxies for the transformed state variables. The methodology is applied to the prices of S&P 500 index options from the period 1996–2005. We find that, in addition to the index value itself, two state variables, approximated by the first two nonlinear principal components, are adequate for pricing the index options and fitting the data in both time series and cross sections.

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