Unspanned Stochastic Volatility in the Multi-Factor CIR Model

Damir Filipović, Martin Larsson and Francesco Statti
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Damir Filipović: Ecole Polytechnique Fédérale de Lausanne and Swiss Finance Institute
Martin Larsson: ETH Zurich
Francesco Statti: Ecole Polytechnique Fédérale de Lausanne

No 17-16, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 (search for similar items in EconPapers)
JEL-codes: C32 G12 G13 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2017-05, Revised 2018-04
New Economics Papers: this item is included in nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1716

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