Correlated VaR: computation, estimation and regulation • Issue: The recent financial crisis enhanced the dramatic implications of erroneous correlation computations in portfolio management. One particular issue is related to the bad computation of the correlation effects within portfolio assets and between them and the exogenous explanatory factors in the computation of the Value at Risk (VaR, from now on), where the explanatory factors can be both observable or latent. • Research Area: Main differences arise while computing the Value at Risk (VaR) with respect to parameters like the probability distribution, the data frequency and the time horizon for the forecast. The issue is ”which variable” best represents the evolution of the portfolio value. Erroneous results are achieved while using false assumptions on multivariate return distribution and therefore on their forecasts: typically independence, no time autocorrelation, nor volatility autocorrelation [Monfort (2008)]. 1. These correlations can be computed by estimating the dependence of this multivariate distribution from one or more explanatory risk factor. These factors can be latent and estimated through Kalman filter [Monfort (2008)] or observable and derived from news at different frequencies [see Calvet 2004 and 2007]. 2. The change of phase in the risk factor can be estimated assuming the regime switching regimes by carefully reducing the number of possible states [see Hamilton 1989, Billio-Pelizzon 2001]. 3. Regulatory policies can be studied and compared to the present Basel II norms. 4. All estimations should be repeated under non normal probability distributions [Meucci (2009), Ibragimov, R. and Walden, J. (2007), Fabozzi et al. (2009), etc. ]. The very important result for the financial industry is that a more accurate estimation of VaR allows a smaller capital collateral thanks to greater sensibility to portfolio volatility. • Statistical Tools: MLE, Kalman filter, Hamilton filter, Latent Markov Chains. • Software tools: Matlab and ”R”.
/ Miceli, Maria Augusta. - (2010).
Miceli, Maria Augusta
Primo
Supervision
2010
Abstract
Correlated VaR: computation, estimation and regulation • Issue: The recent financial crisis enhanced the dramatic implications of erroneous correlation computations in portfolio management. One particular issue is related to the bad computation of the correlation effects within portfolio assets and between them and the exogenous explanatory factors in the computation of the Value at Risk (VaR, from now on), where the explanatory factors can be both observable or latent. • Research Area: Main differences arise while computing the Value at Risk (VaR) with respect to parameters like the probability distribution, the data frequency and the time horizon for the forecast. The issue is ”which variable” best represents the evolution of the portfolio value. Erroneous results are achieved while using false assumptions on multivariate return distribution and therefore on their forecasts: typically independence, no time autocorrelation, nor volatility autocorrelation [Monfort (2008)]. 1. These correlations can be computed by estimating the dependence of this multivariate distribution from one or more explanatory risk factor. These factors can be latent and estimated through Kalman filter [Monfort (2008)] or observable and derived from news at different frequencies [see Calvet 2004 and 2007]. 2. The change of phase in the risk factor can be estimated assuming the regime switching regimes by carefully reducing the number of possible states [see Hamilton 1989, Billio-Pelizzon 2001]. 3. Regulatory policies can be studied and compared to the present Basel II norms. 4. All estimations should be repeated under non normal probability distributions [Meucci (2009), Ibragimov, R. and Walden, J. (2007), Fabozzi et al. (2009), etc. ]. The very important result for the financial industry is that a more accurate estimation of VaR allows a smaller capital collateral thanks to greater sensibility to portfolio volatility. • Statistical Tools: MLE, Kalman filter, Hamilton filter, Latent Markov Chains. • Software tools: Matlab and ”R”.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
