Business — Banking — Management — Marketing & Sales

Transition probabilities map to final asset values, using the standardized distance to default model. Table 38.6 reproduces a transition matrix, with fictitious data. The row F provides all migrations from this credit state to all others, including the default state, the sum of the frequencies as a percentage along the row totalling 100%.

The distribution in Figure 38.6 is extracted from the row, in bold characters, of the full transition matrix showing where an F firm migrates, including to the default state. The distribution of migration probabilities is skewed and the mode is in the same risk class as the initial one, meaning that the absence of migration is the most likely event.

Once the distribution of final states is defined, we have the default probabilities of each rating from historical data. These default probabilities map to the threshold of standardized asset values from a normal standardized distribution. Figure 38.6 shows the corresponding values of the implicit asset threshold triggering default for each migration for which the default probabilities differ from zero. The higher the asset value, the lower the risk, and the larger the downside move of the standardized asset value triggering default. The standardized distance to default results directly from the assigned default probabilities for each final state. For example, when the final state, starting from F, is C, the default probability is 0.1%, requiring a downward move of the standardized distance to default of —3.09, from the standardized normal inverse distribution. When the final state is E, with a probability of migration to this state of 6.1%, the final default probability is 1.5%, and the standardized distance to default is —2.170.

Credit Risk Exposure

Exposures are future amounts at risk. They are valued at book value in the banking portfolio and at market value, or liquidation value, for the trading portfolio. Current exposures are not sufficient to describe exposure risk, since Exposure At Default (EAD) is a future, hence uncertain, exposure. Ideally, the time profile of exposures is the adequate input for measuring risk. This is easy with term loans, with a contractual amortization profile. However, most exposures are uncertain for future dates.

The exposures for the trading portfolio are market-driven and subject to uncertainty as well. For traded instruments, exposure to credit risk remains limited to the holding period. For over-the-counter derivatives, it extends to the entire maturity. Exposure risk relates the uncertainty of future exposures arising from contingent events for the banking portfolio and from market movements for the trading portfolio.

This chapter discusses the exposure measurement for banking products, traded instruments and over-the-counter derivatives.

For the banking portfolio, the on-balance sheet and off-balance sheet exposure uncertainties depend on uncertain events requiring business rules for measurements.

For the market portfolio, exposures are market-driven. For the short holding periods of traded instruments, stocks and bonds, the exposure is the current value, and the credit risk is the fraction of the price variation related to credit risk only. Chapter 43 explains how to isolate these price fluctuations from those related to general market moves.

For over-the-counter derivatives, the exposure is also market-driven, but it extends until maturity. These exposures are two-way exposures. If the liquidation value of the instrument is positive, the bank is at risk, otherwise the counterparty, not the bank, is at risk. Because derivative exposures are market-driven, they vary significantly with time, depending on the volatility of the underlying market parameters. The current risk is the current liquidation value. The potential risk is the time profile is the upper bound of positive exposures, at a given confidence level, as obtained from distributions of values at future time points. These principles follow the guidelines set up by the G30 group.

This chapter comprises three main sections addressing, respectively, exposure uncertainty for banking exposures, tradable instrument exposures and derivative credit exposures. The second section is only an introduction to the detailed discussion of specific risk of tradable instruments in Chapter 43.