# Introduction to Credit Risk Modeling by Bluhm, Christian; Overbeck, Ludger; Wagner, Christoph

By Bluhm, Christian; Overbeck, Ludger; Wagner, Christoph

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81%. Then compute the mean value and the standard deviation of these frequencies over the years, where the rating is fixed, namely m(R) = s(R) = 1 18 1 17 2000 hi (R) and i=1983 2000 i=1983 hi (R) − m(R) 2 . The mean value m(R) for rating R is our first guess of the potential default probability assigned to rating R. The standard deviation s(R) gives us some insight about the volatility and therefore about the error we eventually make when believing that m(R) 6 For example, one could look at investment and sub-investment grades separately.

The first method is based on Monte Carlo simulation; the second is based on a so-called analytical approximation. 8. 1 Monte Carlo Simulation of Losses In a Monte Carlo simulation, losses are simulated and tabulated in form of a histogram in order to obtain an empirical loss distribution of the underlying portfolio. , L ˜ (n) , Assume we have simulated n potential portfolio losses L PF PF hereby taking the driving distributions of the single loss variables and their correlations12 into account.

Risk contributions will be discussed in Chapter 5. An alternative to EC is a risk capital based on Expected Shortfall (ES). A capital definition according to ES very much reflects an insurance point of view of the credit risk business. Today it is known that ES is superior to EC as a risk capital measure for various reasons. We will come back to ES and its properties in Chapter 5. 2 The Loss Distribution All risk quantities on a portfolio level are based on the portfolio loss ˜ P F . Therefore it does not come much as a surprise that variable L ˜ P F , the so-called loss distribution of the portfolio, the distribution of L plays a central role in credit risk management.