CRM 1 - Credit Risk Management Flashcards
Ratings approach to Default Probabilities
- Ratings are expample of Ordinal scale
- Maps a continuous quantity like prob of default into ratings bucket
- Not intended for PD calculation originally
- Meant to have risk on an ordinal scale
Causal Rating Systems approach to Default Probabilities
- Preferred approache
- Rely on a relationship b/w underlying credit risk drivers and default events
- Forces modeler to understand true mechanism of default intead of just relying on various ratios
- Requires customized, specific approaches
- Very powerful and preferred by author
Balance sheet scorings approach to Default Probabilities
- Map balance sheet ratios into scores into PD
Private Client Scorings approach to Default Probabilities
- Conceptually similar to balance sheet scorings
- Except that ratios will computed on different metrics
- Example: wealth, income situation, family context
Expert Rating Systems approach to Default Probabilities
- More complicated situations may require further analysis
- Example: Swiss municipalities had almost no default in a data set analyzed
Overview of Calibration of Default Probabilities to Ratings
- Calibration is the process of assigning default probs to ratings
- Uses historical table of corp bonds defaults by ratings class
- Often best rating classes will have no observed defaults
- Not surprising since expected default prob is very low
Steps in the “quick-and-dirty” calibration of Default Probabilities to Ratings
- Calculate the mean and standard deviation of historical annual default probs
- Mean is first guess for a default prob
- Plot mean values on a coordinate system, with x-axis for rating classes
- use log scale to fit mean default probs to a line since default frequencies grow exponentially w/ decreasing creditworthiness
- Use regression equation to estimate default probs
- Smooth out sampling errors and ensure positive default probs for even best rating classes
Draw-Down Factor (DDF) for Exposure at Default
Analyzes how much of the commitments will be used and is the product of two quantities:
- Prob of commitments getting used?
- If used, how much of the commitments are drawn upon?
Cash Equivalent Exposure Factor (CEEF) for Exposure at Default
- Conversion factor quantifiying the conversion of the specific contigent liability into cash
- Prob of CL generating cash exposure
Overview of contingent liabilities in Exposure at Default
- May not necessarily lead to cash exposure (e.g. an insurer selling guarantees)
- Guarantee has no real exposure as of today, but might in the future
- Prob of contigent liab generating cash exposure = CEEF
Expected Exposure at Default of Contigent Liab
Product of:
- Draw down factor (DDF) of contigent liab
- and, cash equivalent exposure factor (CEEF)
Loss Given Default (LGD)
- 1 minus recovery rate
- Random variable to stimulate severity of a default
Factors impacting recovery rates
- Quality of collateral
- Seniority of bank’s claims
Describe Unexpected Loss when the severity and default event D are uncorrelated
Why is the lack of correlation of severity and default event an unrealistic assumption?
- Default rates spike during bad economies, which is normally when recovery rates drop
- Collateral could also decrease when market drops
Expocted Loss Formula for Portfolio
Unexpected Portfolio Loss
Three correlation cases for portfolio unexpected loss
- If the losses are uncorrelated , then UL attains its minimum
- If the losses are positively correlated, the concentration risk will increase
- If losses could be perfectly negatively correlated, then the UL could be forced equal to zero (unrealisitc in credit risk)
Economic Capital
- Similar to VaR, in that it measures a percentile loss
- Usually quoted in excess of the expected loss
Economic Capital based on confidence interval
- Company may need risk capital for more than one standard deviation of portfolio
Components of Loan Pricing
- Costs of administering loan along with some potential upfront fees
- Expected losses based on the customer credit rating
- Unexpected losses
- dependends on the portfolio because of diversification benefits
Methods to generate credit loss distribution
- Monte carlo simulation:
- Get empirical loss distribution (loss of exposure) from simulations
- Derive risk quantities from empirical distribution
- better captures correlation in portfolio, but takes long time to run
- Analytical approximation:
- Maps an unknown loss distribution to an equivalent portfolio with a known loss distribution
- works well for homogeneous portfolio (e.g. no exposure concentration)
Analytical Approximation steps to generate credit loss distribution
- First choose a family of distributions characterized by its first and second moment (such as a beta distribution)
- From known characteristics of the original portfolio, calculate the first moment (expected loss) and estimate the second moment (unexpected loss)
- Need an average default correlation to calculate the second moment
- Then choose a distribution from the family that most closely matches the first and second moments
- The average asset correlation is critical and difficult to determine
- Can use experience from known portfolios (25% in Moody’s universe of rated corp bonds)
- Calculate the quantiles of the loss distribution as the quantiles of the chosen distribution
Modeling Default Correlations by Means of Factor Models
Identify underlying drivers
Reduces computational efforts for correlated losses
Common factors could include industry or country factors
Express correlation between loans via correlations between factors
The part of the firm’s risk that can be explained by the factors is systematic risk; the other portion of the risk is specific or idiosyncratic risk
Three levels of the KMV factor model
- The first level decomposes the firm’s variance into systematic and specific parts
- The second level decomposes the systematic risk into industry and country risk
- the third level, a weighted sum of independent global factors is constructed for representing industry and country indices
Differences between KMV and CreditMetrics
- KMV is calibrated with asset value processes, while CreditMetrics uses equity
correlations as a proxy for asset correlations - KMV considers industries and countries separately, while CreditMetrics uses indices that are a combination of industry and country.
