Petr Gapko, PhDr., Faculty of Social Sciences, Charles University, Opletalova 26, Prague, 11000, Czech Republic
Risk management is becoming more and more popular and the ongoing financial crisis confirmed it. Particularly large banking institutions face huge fluctuations in earnings and economic losses and thus quantitative risk measurement systems needs to be a common part of the banking business. When speaking about classical commercial or retail banks, economic losses are mainly due to credit risk, i.e. a risk of a counterparty not fulfilling its commitments. Banks are obliged to measure this risk and hold capital to protect against it. The problem arising is how to measure a probability that a customer won’t repay his or her debt? The classical Merton-Vasicek theory (Vasicek 1977) resolves this problem by a measure that satisfies several basic assumptions: normality and Brownian motion of asset returns with a constant volatility. Today these assumptions are treated as unrealistic and we observe several theoretical concepts of describing asset returns that use alternative assumptions such as stochastic volatility and/or Lévy motion (e.g. Merton 1976, Ball 1994, Bates 1996 or Prause 1999). In our work we employ Lévy motion with a class of hyperbolic distributions to describe asset returns behavior. This class of distributions can be fitted to the data by estimating its parameters by maximum likelihood estimator. We will show that such a distribution fits the empirical distribution of asset returns much better than a normal distribution. For this purpose we will employ a Kolmogorov distance as a measure of distribution quality. More accurate distribution gives us a strong instrument for construction of more efficient risk measure, based on Lévy processes. Thus we should be able to calculate capital which is needed to cover credit risk more accurately. In the final part of our work we will test whether the amount of capital calculated by our model fits better real losses (in a whole economy) and discuss the results.