Copulas and bivariate risk measures : an application to hedge funds

With hedge funds, managers develop risk management models that mainly aim to play on the effect of decorrelation. In order to achieve this goal , companies use the correlation coefficient as an indicator for measuring dependencies existing between (i) the various hedge funds strategies and share index returns and (ii) hedge funds strategies against each other. Otherwise, copulas are a statistic tool to model the dependence in a realistic and less restrictive way, taking better account of the stylized facts in finance. This paper is a practical implementation of the copulas theory to model dependence between different hedge fund strategies and share index returns and between these strategies in relation to each other on a "normal" period and a period during which the market trend is downward. Our approach based on copulas allows us to determine the bivariate VaR level curves and to study extremal dependence between hedge funds strategies and share index returns through the use of some tail dependence measures which can be made into useful portfolio management tools.Hedge fund strategies, share index, dependence, copula, tail dependence, bivariate Value at Risk

Implied Risk-Neutral probability Density functions from options prices : A comparison of estimation methods

This paper compares the goodness-of-fit of eight option-based approaches used to extract risk-neutral probability density functions from a high-frequency CAC 40 index options during a normal and troubled period. Our findings show that the kernel estimator generates a strong volatility smile with respect to the moneyness, and the kernel smiles shape varies with the chosen time to maturity. The mixture of log-normals, Edgeworth expansion, hermite polynomials, jump diffusion and Heston models are more in line and have heavier tails than the log-normal distribution. Moreover, according to the goodness of fit criteria we compute, the jump diffusion model provides a much better fit than the other models on the period just-before the crisis for relatively short maturities. However, during this same period, the mixture of log-normal models performs better for more than three month maturity. Furthermore, in the troubled period and the period just-after the crisis, we find that semi-parametric models are the methods with the best accuracy in fitting observed option prices for all maturities with a minimal difference towards the mixture of log-normals model.Risk-neutral density, mixture of log-normal distributions, Edgeworth expansions, Hermite polynomials, tree-based methods, kernel regression, Heston’s stochastic volatility model, jump diffusion model

Copulas and bivariate risk measures: an application to hedge funds

With hedge funds, managers develop risk management models that mainly aim to play on the effect of decorrelation. In order to achieve this goal, companies use the correlation coefficient as an indicator for measuring dependencies existing between (i) the various hedge funds strategies and share index returns and (ii) hedge funds strategies against each other. Otherwise, copulas are a statistic tool to model the dependence in a realistic and less restrictive way, taking better account of the stylized facts in finance. This paper is a practical implementation of the copulas theory to model dependence between different hedge fund strategies and share index returns and between these strategies in relation to each other on a "normal " period and a period during which the market trend is downward. Our approach based on copulas allows us to determine the bivariate VaR level curves and to study extremal dependence between hedge funds strategies and share index returns through the use of some tail dependence measures which can be made into useful portfolio management tools

On the study of conditional dependence structure between oil, gold and USD exchange rates

International audienc

Is the role of precious metals as precious as they are? Revisiting the role of precious metals for the G-7 stock markets: A multivariate vine copula and BiVaR approaches.

This paper revisits the international evidence on hedge, safe haven and diversificationproperties of precious metals, namely; gold, silver and platinum for the G-7 stock marketswhereas most of the studies have focused only on gold properties. Conversely to the studies in the literature that use only bivariate copula, we use the multivariate vine copula based GARCH model. We then find that precious metals have valuable hedge and safe haven roles with different degrees. Our findings show that gold is the strongest hedge and safe haven asset, in almost all the G-7 stock markets. For silver and platinum, results show that they may act as weak hedge assets. Also, silver bear the potential of a strong safe haven role only for Germany and Italy stock markets. However, platinum provides weak safe haven role for most developed stock markets. Using the Bivariate VaR risk measure, we suggest that precious metals may offer diversification benefits in the G-7 stock markets

Is the role of precious metals as precious as they are? Revisiting the role of precious metals for the G-7 stock markets: A multivariate vine copula and BiVaR approaches.

This paper revisits the international evidence on hedge, safe haven and diversificationproperties of precious metals, namely; gold, silver and platinum for the G-7 stock marketswhereas most of the studies have focused only on gold properties. Conversely to the studies in the literature that use only bivariate copula, we use the multivariate vine copula based GARCH model. We then find that precious metals have valuable hedge and safe haven roles with different degrees. Our findings show that gold is the strongest hedge and safe haven asset, in almost all the G-7 stock markets. For silver and platinum, results show that they may act as weak hedge assets. Also, silver bear the potential of a strong safe haven role only for Germany and Italy stock markets. However, platinum provides weak safe haven role for most developed stock markets. Using the Bivariate VaR risk measure, we suggest that precious metals may offer diversification benefits in the G-7 stock markets