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Hedging (Co)Variance Risk With Variance Swaps


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    (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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Bibliographic Info

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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Keywords: Wishart Affine Stochastic Correlation model; complete and incomplete markets; variance swaps; Fourier transform;


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Cited by:
  1. Da Fonseca, José & Gnoatto, Alessandro & Grasselli, Martino, 2013. "A flexible matrix Libor model with smiles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 774-793.
  2. Alessandro Gnoatto & Martino Grasselli, 2011. "The explicit Laplace transform for the Wishart process," Papers 1107.2748,, revised Aug 2013.
  3. Branger, Nicole & Muck, Matthias, 2012. "Keep on smiling? The pricing of Quanto options when all covariances are stochastic," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1577-1591.
  4. Schürhoff, Norman & Ziegler, Alexandre, 2011. "Variance risk, financial intermediation, and the cross-section of expected option returns," CEPR Discussion Papers 8268, C.E.P.R. Discussion Papers.
  5. Giovanni Salvi & Anatoliy V. Swishchuk, 2012. "Modeling and Pricing of Covariance and Correlation Swaps for Financial Markets with Semi-Markov Volatilities," Papers 1205.5565,
  6. Alessandro Gnoatto, 2012. "The Wishart short rate model," Papers 1203.5513,, revised May 2014.
  7. Jan Baldeaux & Eckhard Platen, 2012. "Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods," Papers 1204.1126,


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