Measuring market risk though value at riskthe the role of fat-tail and skewness distributions in VaR estimate and loss functions in models comparison

Laburpena

One of the most important tasks that financial institutions face is to measure any asset exposure to market risk. This risk arises as a result of the changes that may suffer the price of the assets that encompass a portfolio. One of the possible measures to quantify this risk is the evaluation of losses likely to be incurred when the price of the portfolio assets falls. This is what Value al Risk (VaR) undertakes. Since the BCBS al the Bank for International Settlements requires a financial institution to meet capital requirements on the basis of VaR estimates, allowing them to use internal models for VaR calculations, this measurement has become a basic market risk management tool for financial institutions. Consequently, it is of not surprise that the last decade has witnessed the growth of academic literature comparing alternative modelling approaches and proposing new models for VaR estimations in an attempt to improve upon those already in existence. The success of VaR is based on the fact that it is essentially a simple concept, since the VaR reduces the risk associated with a portfolio to a single number. But despite this simplicit, its statistical measurement remains today a challenge. Therefore, over the years different methodologies have been developed for obtaining more accurate VaR estimates. Thus, the main objectives pursued by this thesis are the following: 1.- The first goal in this Thesis (Chapter 2) is to conduct thorough theoretical review of existing methodologies, showing the strengths and weaknesses presented on each of them. Additionally, since there is no consensus on the best approach, a summary of the empirical results obtained by works devoted to the comparison of VaR methodologies is displayed. 2.- The second objective (Chapter 3) is the evaluation of the accuracy of some skewed and fat-tail distributions for the purpose of the VaR estimation. A comparison of a wide range of symmetric and asymmetric distributions is conducted. For such purpose, an empírical analysis using data of the main European, Americans and Asians stock indices have been performed. The comparative is addressed following two directions: first, the distributions are compared in statistical terms to determine which it is the best for fitting financial return in second place, the distributions are compared in terms of VaR, in order to select which is best for forecasting VaR. 3° As important as measuring market risk is to analyze the results of estimations generated, i.e. what is known by the ten "backtesting". Risk managers need a tool or formal procedure that allows them to analyze the VaR measure results as they are interested in choosing the best model among different alternative VaR measures. Backtesting procedures can be broadly classified into two groups: backtesting based on any statistical test and backtesting based on a loss function. The third goal of the Thesis Chapter 4) is to examine whether the comparison of VaR models depends on the loss function used for such purpose. To do so, a comparison of different VaR models using the loss functions proposed by the literature is carried out, taking into account both regulators and company risk managers concerns, and eventually checking if the results of these comparisons are robust to the loss function used. Additionally, a new firms loss function has been proposed, which has the advantage of of re covered. Finally, the Thesis ends with some concluding remarks shown in the Chapter 5.