Unspanned Stochastic Volatility in the Multifactor CIR Model

10 Pages Posted: 28 May 2020

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Martin Larsson

ETH Zürich - Department of Mathematics

Francesco Statti

Ecole Polytechnique Fédérale de Lausanne

Date Written: July 2019

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, Journal of Finance, 57, 1685–1730) 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 multifactor 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 multifactor CIR models with diagonal drift matrix cannot exhibit USV.

Keywords: incomplete bond markets, multifactor Cox–Ingersoll‐Ross model, unspanned stochastic volatility

Suggested Citation

Filipovic, Damir and Larsson, Martin and Statti, Francesco, Unspanned Stochastic Volatility in the Multifactor CIR Model (July 2019). Mathematical Finance, Vol. 29, Issue 3, pp. 827-836, 2019, Available at SSRN: https://ssrn.com/abstract=3613158 or http://dx.doi.org/10.1111/mafi.12193

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 Zürich - 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

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