Hedging (Co)Variance Risk with Variance Swaps

46 Pages Posted: 19 Feb 2009

See all articles by José Da Fonseca

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Florian Ielpo

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES); Unigestion

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Multiple version iconThere are 2 versions of this paper

Date Written: February 12, 2009

Abstract

In this paper we measure the impact of variance and covariance risks in financial markets. In an asset allocation framework with stochastic (co)variances, we consider the possibility to invest not only in the risky assets but also in the variance swaps associated that are non redundant derivatives which span the volatility as well as the co-volatility risks. We provide explicit solutions for the portfolio optimization problem in both the incomplete and completed market cases. We use the ratio between the initial wealths leading to the same expected utility in the two market cases as a criterion in order to measure the impact of (co)variance risk. Using real data on major indexes and this criterion, we find that the impact of (co)variance risk on the optimal strategy is huge. We especially discuss the sensitivity of the criterion proposed to measure (co)variance risk with respect to the volatility of volatility parameter and it is found to be huge. This is consistent with the single asset empirical literature and the fast development of variance and covariance-based derivative products.

Keywords: Wishart Affine Stochastic Correlation model, complete and incomplete markets, variance swaps, optimal portfolio choice with derivatives

JEL Classification: G11, G12

Suggested Citation

Da Fonseca, José and Ielpo, Florian and Grasselli, Martino, Hedging (Co)Variance Risk with Variance Swaps (February 12, 2009). Available at SSRN: https://ssrn.com/abstract=1341811 or http://dx.doi.org/10.2139/ssrn.1341811

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

Florian Ielpo

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES) ( email )

106-112 Boulevard de l'hopital
106-112 Boulevard de l'Hôpital
Paris Cedex 13, 75647
France

Unigestion ( email )

8c, avenue de Champel CP 387
CP 387
Genève 12, CH 1211
Switzerland

Martino Grasselli (Contact Author)

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

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