23. Analysing credit risk Flashcards
Define credit risk
- Risk of loss due to contractual obligations not being met (in terms of quantity, quality or timing) either in part/in full whether due to inability or by decision
What are the two components
- Default risk
- Credit spread risk
Which give examples of credit risk events?
Missed payment
Financial ratio falling below some level
Legal proceedings starting against credit issuer
Present value of A falls below L because of economic factors
What are the two components of default risk
Probability of default
Loss on default
What are the 3 things that must be assessed when assessing default risk
Probability of default
Loss on default
Level and nature of interactions between credit exposures and other risks in a portfolio
Identify sources of information for credit risk
- Credit rating agencies
- Counterparty
- Publicly available data
- Proprietary databases
Outline the items that qualitative assessments of credit risk can be based on
o Nature of contract e.g. seniority of a loan
o Level and nature of security e.g. parental guarantees, collateral
o Nature of borrower e.g. industry sector / employment status
o Economic indicators
o Financial ratios
o Face to face meetings with credit issuer and/or counterparty
Outline the merits of qualitative risk assessments
Advantages:
o Range of (subjective) factors can be incorporated into assessment
Disadvantages:
o Excessive subjectivity
o Inconsistency between ratings
o Meaning of subjective ratings could change over eco cycle and/or due to changes in eco environment
o Ratings might fail to respond to changing eco cycles or circumstances of counterparty- often reluctance to change rating
List examples of quantitative credit models
- Credit scoring
- Structural models
- Reduced form models
- Credit portfolio models
- Credit exposure models
Describe credit scoring models
- Use fundamental info to get likelihood of default
- E.g.
o Empirical models
o Expert models
Outline structural models
- AKA Firm value
- Use share price and volatility
- E.g., KMV and Merton
Explain how the Merton model works
o Uses Black-Scholes option pricing theory along with equity share price volatility to get info on value of total A and value of D
o Considers total A = total E + total D
o D is zero-coupon bond redeemable at some future t
o Total A assumed to follow geometric Brownian motion (continuous-time lognormal random walk)
o Shareholders can be thought of as call option holders of total A
o If A > nominal value of D by t then D repaid and sh get residual A
o Nominal value of D is strike price of call
o If A < nominal value of D by t then sh get nothing aka call not exercised
o Equity shares are like call options and can be valued using option-pricing theory and B-S
o D valued as diff between A and E
o Equivalentlt, by Put-call parity, value of D = value of risk free bond – value of put on company’s total A
o Idea: if A increase in value, bh get same amount at maturity as holder of risk free bond
o If A<nominal value of D, equity sh default and bh lose diff between total A at redemption and nominal value of D
Outline the pros of the Merton model
Mathematically tractable using B-S option pricing results
Intuitive results, eco explanation for P(default) as based on capital structure of co and changes in co value
Can estimate appropriate credit spread for bond if unquoted or unrated
Outline the cons of the Merton model
- Assumptions of:
Frictionless markets (no transaction costs) with continuous trading
Risk free rate deterministic and constant for borrowers and lenders
X_t follows lognormal random walk with fixed growth rate and volatility independent of firm financial structure which is unrealistic assumption
Bond is zero-coupon with one defalt opportunity
Default = liquidation- can mean diff things in real life - Can only be solved when X_t and sigma are observable- impossible
- Accurate sigma estimate needed»_space; more appropriate for larger cos with frequently traded stocks
- Results sensitive to market sentiments in absence of real changes
Outline how the KMV model works
o Uses Merton’s concept: company will default first instance X_t falls below (or some B^ based on term structure of liabilities, usually 1 year L)
o Distance to Default(DD): # of std deviations company’s A must fall in value before breaching B
DD(t)=[X(t)-B]/[X(t)*σ(x)]
o Use empircal data on co defaults and how linked to DD to get P(Default)
Outline how the KMV model is better than the Merton model
Coupon-paying bonds can be modelled
More complex L structures can be accommodated as system uses average and overall gearing level (rather than having to assume sing zero-coupon bond)
X(t) not assumed to be observable and derived from co’s equity shares.
Outline what reduced-form models are
- Model default as statistical process dependent on eco variables
- E.g., Credit migration models
Outline how credit migration models work
o For longer term exposures
o E.g. 2 state model and Jarrow-Lando-Turnbull
o Estimate probability:
Historical data use to determine probability that co moves to lower rating at end of year and probs recorded in transition probability matrices
Matrices applied to counterparty’s current rating to estimate likelihood of each possible rating in each future year
Use prob of default for company of given rating to estimate chance of default in each year
Outline the merits of credit migration models
Pros:
Volatile equity markets shouldn’t overly affect results – makes sense as empirically, this is usually the case
Cons- assumptions:
Likelihood of default determined just by credit rating
Credit rating reflect average company’s default likeligood throughout business cycle (instead of reflecting chance in current eco environment)
Follows time-homogeneous Markov chain- assumption that history will repeat
Outline hw credit portfolio models work
- Estimate credit exposure over many counterparties
- May allow for diversification and aggregation
- Key challenge is allowing for these relationships
Give examples of credit portfolio models
- Multivariate structural
- Multivariate credit migration models
- Econometric
- Common shock models
Outline how multivariate structural models work
- Multivariate KMV, using correlation matrices to model A values or copulas (t or explicit fat tailed)
Outline how multivariate credit-migration models
- E.g. CreditMetrics
- Assumes equity returns can be modelled by country-specific indices and independent firm-specific volatility
- Monte Carlo simulations used to derive potential:
o Movements in equity values
o Corr changes in overall value of each org’s assets
o Associated rating changes
o Implied change in value of bonds in portfolio (incl. default experience) - Can apply risk measures to the simulations
What are the assumptions underlying the CreditMetrics model
o Each credit rating has associated P(Default)
o Change in rating is function of change in value of org’s assets and volatility value of those assets
o Value of assets of each org in portfolio behaves log-normally
o Correlation between asset values (of diff orgs) can be estimated from correlation between corr equity values
o Equity returns can be modelled by country-specific indices and firm specific volatility
Define econometric models, common shoch models and time until default
Econometric/actuarial models
* Don’t model asset value going forward- estiate default rate using external (e.g. economic) or empirical data
Common shock models
* Determine P(no defaults) assuming each bond defaults in line with Poisson process, and considering shocks, each of which cause default of one or more of bonds in portfolio
Time-until-default / survival models
* Survival CDFS (each based on hazard rate determined from implied probability of default) are linked by suitably parametrised copula function, so as to estimate aggregate default rate for bond portfolio.
Give an example of credit exposure models
Monte Carlo approach to estimate expected and max credit exposures
Give high level problems with modelling credit risk
- Lack of publicly available info/data on credit quality of individual companies- companies may choose not to pay for rating or publish any ratings.
- Skewness of credit loss distributions. Typically have heavy tails where losses are greatest- making it difficult to estimate extreme events
- Dependence of one credit event on others. If one counterparty defaults, often found that other connected companies or those in similar industry also default. Assumptions on dependency have big impact on overall results of models.
- Some economic events have no equivalent in history, data difficult to get.
Why is a lack of data a problem
- Difficult to calibrate models
What are the effects of not being able to estimate extreme events?
o Makes it difficult to estimate capital requirements
Explain why dependence is an issue in modelling
o Dependency caused by economic links between companies, which can be exposed to similar macroeconomic factors. So default events can be triggered by particular set of eco circumstances.
o Obtaining reliable data on the dependency is difficult
What determines recoveries
o Seniority of debt
o Rights of other creditors
o Availability of (marketable/liquid) collateral
