Option Implied VIX, Skew and Kurtosis Term Structures

16 Pages Posted: 20 Aug 2020 Last revised: 26 Dec 2020

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: July 17, 2020

Abstract

Comparisons are made of the CBOE skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies may be attributed to strike discretization in evaluating prices of powered returns. The remedy suggested employs a finer and wider set of strikes obtaining additional option prices by interpolation and extrapolation of implied volatilities. Procedures of replicating powered return claims are applied to the fourth power and the derivation kurtosis term structures. Regressions of log skewness and log excess kurtosis on log maturity confirm the positivity of decay in these higher moments. The decay rates are below those required by processes of independent and identically distributed increments.

Keywords: Characteristic Exponent, Bilateral Gamma Model, Self Decomposable Law, Sato Process

JEL Classification: G10, G11, G12.

Suggested Citation

Madan, Dilip B. and Wang, King, Option Implied VIX, Skew and Kurtosis Term Structures (July 17, 2020). Available at SSRN: https://ssrn.com/abstract=3654563 or http://dx.doi.org/10.2139/ssrn.3654563

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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