Pricing Options on Realized Variance

26 Pages Posted: 11 Mar 2005 Last revised: 30 Jan 2010

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Hélyette Geman

University of London - Economics, Mathematics and Statistics

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Marc Yor

Universite Paris

Date Written: January 26, 2005

Abstract

Models which hypothesize that returns are pure jump processes with independent increments have been shown to be capable of capturing the observed variation of market prices of vanilla stock options across strike and maturity. In this paper, these models are employed to derive in closed form the prices of derivatives written on future realized quadratic variation. Alternative work on pricing derivatives on quadratic variation has alternatively assumed that the underlying returns process is continuous over time. We compare the model values of derivatives on quadratic variation for the two types of models and find substantial differences.

Keywords: Options on Variance Swaps, Options on Time Changes, Self Decomposability and its Hierarchy

JEL Classification: G10, G12, G13

Suggested Citation

Carr, Peter P. and Geman, Helyette and Madan, Dilip B. and Yor, Marc, Pricing Options on Realized Variance (January 26, 2005). EFA 2005 Moscow Meetings Paper. Available at SSRN: https://ssrn.com/abstract=684087 or http://dx.doi.org/10.2139/ssrn.684087

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Helyette Geman (Contact Author)

University of London - Economics, Mathematics and Statistics ( email )

Malet Street
London, WC1E 7HX
United Kingdom

Dilip B. Madan

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)

Marc Yor

Universite Paris ( email )

223 Rue Saint-Honore
Paris, 75775
France

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