Unspanned Stochastic Volatility in the Multi-Factor CIR Model

Mathematical Finance, Forthcoming

Swiss Finance Institute Research Paper No. 17-16

15 Pages Posted: 8 May 2017 Last revised: 16 Jan 2019

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Martin Larsson

ETH Zurich - Department of Mathematics

Francesco Statti

Ecole Polytechnique Fédérale de Lausanne

Date Written: April 13, 2018

Abstract

Empirical evidence suggests that fixed income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While Collin-Dufresne and Goldstein (2002) showed that no two-factor Cox-Ingersoll-Ross (CIR) model can exhibit USV, it has been unknown to date whether CIR models with more than two factors can exhibit USV or not. We formally review USV and relate it to bond market incompleteness. We provide necessary and sufficient conditions for a multi-factor CIR model to exhibit USV. We then construct a class of three-factor CIR models that exhibit USV. This answers in the affirmative the above previously open question. We also show that multi-factor CIR models with diagonal drift matrix cannot exhibit USV.

Keywords: multi-factor Cox-Ingersoll-Ross model, unspanned stochastic volatility, incomplete bond markets

JEL Classification: C32, G12, G13

Suggested Citation

Filipovic, Damir and Larsson, Martin and Statti, Francesco, Unspanned Stochastic Volatility in the Multi-Factor CIR Model (April 13, 2018). Mathematical Finance, Forthcoming; Swiss Finance Institute Research Paper No. 17-16. Available at SSRN: https://ssrn.com/abstract=2964751 or http://dx.doi.org/10.2139/ssrn.2964751

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

Martin Larsson

ETH Zurich - Department of Mathematics ( email )

Ramistrasse 101
Zurich, 8092
Switzerland

HOME PAGE: http://math.ethz.ch/~larssonm

Francesco Statti

Ecole Polytechnique Fédérale de Lausanne ( email )

Station 5
Odyssea 1.04
1015 Lausanne, CH-1015
Switzerland

Register to save articles to
your library

Register

Paper statistics

Downloads
144
Abstract Views
877
rank
203,563
PlumX Metrics