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Hedging (Co)Variance Risk With Variance Swaps



    (Auckland University of Technology, Department of Finance, Private Bag 92006, 1142 Auckland, New Zealand)



    (Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via Trieste 63, Padova, Italy; Ecole Supérieure d'Ingénieurs Léonard de Vinci, Département Mathématiques et Ingénierie Financière, 92916 Paris La Défense, France)



    (Lombard Odier Darier Hentsch & Cie, rue de la Corraterie 11, CH-1204 Genève 73, Switzerland)

In this paper, we quantify the impact on the representative agent's welfare of the presence of derivative products spanning covariance risk. In an asset allocation framework with stochastic (co)variances, we allow the agent to invest not only in the stocks but also in the associated variance swaps. We solve this optimal portfolio allocation program using the Wishart Affine Stochastic Correlation framework, as introduced in Da Fonseca, Grasselli and Tebaldi (2007): it shares the analytical tractability of the single-asset counterpart represented by the [36] model and it seems to be the natural framework for studying multivariate problems when volatilities as well as correlations are stochastic. What is more, this framework shows how variance swaps can implicitly span the covariance risk. We provide the explicit solution to the portfolio optimization problem and we discuss the structure of the portfolio loadings with respect to model parameters. Using real data on major indexes, we find that the impact of covariance risk on the optimal strategy is huge. It first leads to a portfolio that is mostly driven by the market price of volatility-covolatility risks. It is then strongly leveraged through variance swaps, thus leading to a much higher utility, when compared to the case when investing in such derivatives is not possible.

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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 14 (2011)
Issue (Month): 06 ()
Pages: 899-943

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Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:06:p:899-943
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