Quadratic Variance Swap Models

77 Pages Posted: 23 Mar 2013 Last revised: 20 Dec 2014

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Elise Gourier

ESSEC Business School

Loriano Mancini

USI Lugano - Institute of Finance; Swiss Finance Institute

Date Written: December 18, 2014

Abstract

We introduce a novel class of term structure models for variance swaps. The multivariate state process is characterized by a quadratic diffusion function. The variance swap curve is quadratic in the state variable and available in closed form, greatly facilitating empirical analysis. Various goodness-of-fit tests show that quadratic models fit variance swaps on the S&P 500 remarkably well, and outperform affine models. We solve a dynamic optimal portfolio problem in variance swaps, index option, stock index and bond. An empirical analysis uncovers robust features of the optimal investment strategy.

Keywords: stochastic volatility, variance swap, quadratic term structure, quadratic jump-diffusion, dynamic optimal portfolio

JEL Classification: C51, G13

Suggested Citation

Filipovic, Damir and Gourier, Elise and Mancini, Loriano, Quadratic Variance Swap Models (December 18, 2014). Journal of Financial Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2237512 or http://dx.doi.org/10.2139/ssrn.2237512

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Elise Gourier

ESSEC Business School ( email )

3 avenue Bernard Hirsch
Cergy-Pontoise, 95021
France

HOME PAGE: http://www.elisegourier.com

Loriano Mancini

USI Lugano - Institute of Finance ( email )

Via Giuseppe Buffi 6
6904 Lugano, CH-6904
Switzerland
+41 (0)91 912 46 47 (Fax)

HOME PAGE: http://www.people.usi.ch/mancil/

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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