Multi-Asset Stochastic Local Variance Contracts

32 Pages Posted: 30 Dec 2010

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Peter M. Laurence

University of Rome I - Department of Mathematics; Courant Institute, NYU

Date Written: September 22, 2010

Abstract

Variance swaps now trade actively over-the-counter (OTC) on both stocks and stock indices. Also trading OTC are variations on variance swaps which localize the payoff in time, in the underlying asset price, or both. Given that the price of the underlying asset evolves continuously over time, it is well known that there exists a semirobust hedge for these localized variance contracts. Remarkably, the hedge succeeds even though the stochastic process describing the instantaneous variance is never specified. In this paper, we present a generalization of these results to the case of two or more underlying assets.

Keywords: variance swap, basket option, stochastic volatility

Suggested Citation

Carr, Peter P. and Laurence, Peter M., Multi-Asset Stochastic Local Variance Contracts (September 22, 2010). Mathematical Finance, Vol. 21, Issue 1, pp. 21-52, 2010. Available at SSRN: https://ssrn.com/abstract=1732469 or http://dx.doi.org/10.1111/j.1467-9965.2010.00422.x

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

Peter M. Laurence

University of Rome I - Department of Mathematics ( email )

Roma, I-00185
Italy

Courant Institute, NYU ( email )

Division of Quantitative Finance 251 Mercer Street
New York, NY 10012
United States
212 9983000 (Phone)
212 9954121 (Fax)

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