Quadratic Variation

31 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: December 26, 2020

Abstract

Time changes of Brownian motion impose restrictive jump structures in the motion of asset prices. Quadratic variations also depart from time changes. Joint Laplace Fourier transforms for quadratic variation and the stock are developed. They are used to study the multiple of the cap strike over the variance swap quote attaining a given percentage price reduction for the capped variance swap. Bootstrapped data and simulated paths spaces are used to study the multiple of the dynamic hedge return desired by a realized variance swap contract. The optimized hedge multiple in the bootstrapped data is consistently near unity. Simulated path spaces allow for departures matched by also similarly altering the position in the log contract. Value multiples of quadratic variation over variance swaps are consistently larger in simulations and bootstrapped data. The departures reflect negative dividend yields embedded in the skewness of risk neutral distributions.

Keywords: Bilateral Gamma, Sato Process, Volatility of Variance, Self Decomposable Laws, Sato Lévy Mixtures

JEL Classification: G10, G12, G13

Suggested Citation

Madan, Dilip B. and Wang, King, Quadratic Variation (December 26, 2020). Available at SSRN: https://ssrn.com/abstract=3755363 or http://dx.doi.org/10.2139/ssrn.3755363

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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