Option Surface Econometrics with Applications

18 Pages Posted: 23 Feb 2021

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

King Wang

Morgan Stanley

Date Written: January 18, 2021

Abstract

At each maturity a discrete return distribution is inferred from option prices. Option pricing models imply a comparable theoretical distribution. As both the transformed data and the option pricing model deliver points on a simplex, the data is statistically modeled by a Dirichlet distribution with expected values given by the option pricing model. The resulting setup allows for maximum likelihood estimation of option pricing model parameters with standard errors enabling the test of hypotheses. Hypothesis testing is illustrated by testing for risk neutral return distributions being consistent with Brownian motion with drift time changed by a subordinator. Models mixing processes of independent increments with processes related to solution of Ornstein Uhlenbeck (OU) equations are tested for the presence of the OU component. OU equations are a form of perpetual motion processes continuously responding to their past changes. The tests support the rejection of Brownian subordination and the presence of a perpetual motion component.

Keywords: Bilateral Gamma, Tempered Stable, Self Decomposable, Sato Process

JEL Classification: G11, G12, G13

Suggested Citation

Madan, Dilip B. and Wang, King, Option Surface Econometrics with Applications (January 18, 2021). Available at SSRN: https://ssrn.com/abstract=3768817 or http://dx.doi.org/10.2139/ssrn.3768817

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)

King Wang

Morgan Stanley ( email )

1585 Broadway
New York, NY 10036
United States

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