HEDGING (CO)VARIANCE RISK WITH VARIANCE SWAPS

José Da Fonseca, Martino Grasselli () and Florian Ielpo
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Martino Grasselli: Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via Trieste 63, Padova, Italy;

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 06, 899-943

Abstract: 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.

Keywords: Wishart Affine Stochastic Correlation model; complete and incomplete markets; variance swaps; Fourier transform (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (13)

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DOI: 10.1142/S0219024911006784

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