Measuring the Distribution of Credit Losses

We can now pool together the information on default probabilities, credit exposures, and recovery rates to measure the distribution of losses due to credit risk. For simplicity, we only consider losses in default mode (DM), that is, due to defaults instead of changes in market values. For one instrument, the current or potential credit loss is Credit Loss b X Credit Exposure X LGD (23.1) which involves the random variable b that takes on the value of 1, with probability p, when the discrete...

The Time Profile of Expected Loss

So far, we have focused on a fixed horizon, say a year. For pricing purposes, however, we need to consider the total credit loss over the life of the asset. This should involve the time profile of the exposure, of the probability of default, and the discounting factor. Define PVf as the present value of a dollar paid at t. The present value of expected credit losses (PVECL) is obtained as the sum of the discounted expected credit losses, PVECL E CLt x PVt kt x ECEt x (1 - f) x PVt (23.7) where...

Correlations among defaults

Correlations among defaults are inferred from correlations between asset prices. Each obligor is assigned to an industry and geographical sector, using a factor decomposition. Correlations are inferred from the comovements of the common risk factors, using a database with some 152 country-industry indices, 28 country indices, and 19 worldwide industry indices. As an example, company 1 may be such that 90 of its volatility comes from the U.S. chemical industry. Using standardized returns, we can...

FIGURE 206 KMVs EDF and Credit Rating

July 21, 2002 Bankruptcy of default rating July 21, 2002 Bankruptcy of default rating Figure 20-6 displays movements in EDFs and credit rating for Worldcom, using the same vertical scale. Worldcom went bankrupt on July 21, 2002. With 104 billion in assets, this was America's largest bankruptcy ever. The agency rating was BBB until April 2002. It gives no warning of the impending default. In contrast, starting one year before the default, the EDF starts to move up. In April, it reached 20 ,...

Black Scholes Valuation

Black Scholes Probability Curve

We now briefly introduce the pricing of conventional European call and put options. Initially, we focus on valuation. We will discuss sensitivities to risk factors later, in Chapter 15 that deals with risk management. To illustrate the philosophy of option pricing methods, consider a call option on a stock whose price is represented by a binomial process. The initial price of S0 100 can only move up or down, to two values hence the bi , S1 150 or S2 50. The option is a call with K 100, and...