S&P 500 Index Option Surface Drivers and their Real World and Risk Neutral Covariations

35 Pages Posted: 20 Sep 2010 Last revised: 20 Nov 2010

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: September 29, 2010

Abstract

Observing first that the daily option surface may be summarized by the level of the spot price and the four parameters of the Sato process based on the variance gamma process, a time series is constructed for this five dimensional set of factors driving the surface of S&P 500 index option prices. Next we show that parameter movements can be hedged at zero cost and a delta hedged position then earns in its theta compensation for the exposure to the fifteen second order squared and cross product terms. The coefficients of compensation form an estimate for the risk neutral quadratic covariation between the five surface drivers. A constrained optimization forcing positive semidefinite coefficients is then employed to estimate risk neutral covariations. Simultaneously statistical covariations are estimated and it is shown that the two sets of covariations are quite different. We then ask if quadratic variations in all directions risk neutrally exceed their statistical counterparts. This is not the case and quadratic variations of the stock price unaccompanied by other movements of the surface have a lower risk neutral expectation. All other directions have a higher risk neutral quadratic variation from their statistical counterparts.

Keywords: Background PDE, Sato Process, Trading Parameters, Constraining for positive semidefiniteness

JEL Classification: G10, G12, G13

Suggested Citation

Madan, Dilip B., S&P 500 Index Option Surface Drivers and their Real World and Risk Neutral Covariations (September 29, 2010). Robert H. Smith School Research Paper No. RHS 06-130. Available at SSRN: https://ssrn.com/abstract=1679524 or http://dx.doi.org/10.2139/ssrn.1679524

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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