WEEK 7:

CORPORATE CREDIT RISK MODELS BASED ON STOCK PRICE

FIRST PRESENTATION
Q1: The major development in finance in the last 30 years is the options pricing theory.
Why is this so?
Miller and Modigliani (MM) considered the investment decision and the financing decision as
separate. A given investment plan implied a stream of expected cash flows for the firm, and that
implied a market value for the firm today. This made the market value of the firm into the
underlying firm characteristic. The market value of the firm’s debt, equity, and other liabilities
derived from the overall value of the firm and these, taken together, added up to the firm value.

The expected operating cash flows of the firm determined its overall value; the capital structure
merely represented the division of these cash flows to providers of capital. For instance, more
debt means that debt holders provided more capital and received more of a firm’s cash flows.
However, it did not intrinsically raise or lower the value of the firm because it was considered
separately from the investment program.

Unfortunately, at the time of MM there was no known way to separately determine the debt and
equity values. By the rules of debt, debt holders are paid before equity holders; debt has
seniority. No method existed for determining the value of the debt as a senior claim on the firm’s
cash flows, nor equity as a junior claim. The world had to wait for the development of options
pricing theory.

Q2: Explain why equity is like a call option

The equity of the firm has exactly the same payoff as a call option on the same amount of stock
as held by the firm, with an aggregate exercise price of D. In that case, the option would be
exercised when the stock was worth more than D, and the payoff would be the difference
between the stock value and D; and otherwise the option would be worthless. In other words, the
equity of the firm is a call option on the assets of the firm, where the exercise price and maturity
are given by the face value and maturity of the debt.

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We could explicitly value the equity of this firm if we knew the face value and the maturity of
the debt, the value of the assets today and the volatility of the assets. For this simple example, we
could actually use the Black-Scholes option pricing formula. For more complicated cases, we
could not use the BS method but we could use their general approach to obtain a value for the
equity of the firm.

From the standpoint of credit analysis, the interesting point is that default can be thought of as
failure of exercise an option. Equity holders ‘optionally’ own the firm, but if the firm does poorly
enough, they do not exercise their option, but rather allow the firm’s ownership to pass to the
debt holders in lieu of paying the debt service.

Q3: Explain why debt is like selling a put option.

The equity holders own the asset, have borrowed D, but own a put that enables them to sell the
assets for D. In essence, the debt holders of the firm, at the same time that they lent to the firm,
by recognizing the possibility of default, have also ‘sold’ a put option to the equity holders. The
put enables the equity holders to ‘put’ them the assets in lieu of paying off the debt. Thus the
firm’s debt is like a default risk-free loan of the amount D less a put option. In this case, the
event of default is identical to the exercise of the put option by the equity holders.

The firm’s debt is always worth less than default risk-free because it is ‘short’ a put option. The
greatest is the default risk of the firm, the more valuable is the put option, and the less valuable is
the debt since it is short the put option. Debt subject to default risk can be decomposed into
default risk-free debt and a put option. In doing credit analysis, the focus is on understanding the
value of the put option and the probability of it being exercised.

SECOND PRESENTATION
Q4: Refer to Figure 11.1 on page 187.
4.1 What does the x and y-axis represent in the graph?
The y-axis represents the market value of the firm in dollar terms with the x-axis representing the
time horizon.
4.2 What does the bell shape represent?

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The bell shape distribution is a representation of the future asset value of time, i.e. if the firm
borrows money and invests in assets and what is the probability for the firm to achieve certain
market values over the time period. As like any normal distribution curve, it is very unlikely that
the firm achieves both very high and very low market values. There is more of a probability that
the firm will achieve an average market value, hence why we have a normal distribution.
4.3 There is a straight line cutting through the bottom part of the normal distribution.
What does this represent?
The line parallel to the x-axis with an increase further on is the firm’s liabilities outstanding at a
point in time. As long as the liabilities are lower than the market value the firm is solvent. The
firm starts getting in financial distress when the asset value starts to drop towards the straight
line. The increase in the straight line represents the increase in debt outstanding. This can be the
interest accrued or else an increase in loan.
4.4 So what happens when the standard deviation (SD) of the future asset values is close
to the straight line (debts outstanding)?
It is a concern when the SD is small because what it means is that it does not take much for the
firm to be financially distressed.
4.5 What does the dotted line represent?
The dotted line represents the firm’s net expected growth of assets as a consequence of incurring
debt. If the dotted line is sloping downwards then the firm will be in financial distress. A steeper
curve represents a healthier firm.
4.6 How are the following two values found: market value of the assets (V) and the
volatility of the assets (σ)?
There are the following two equations (Eq 11.2 and 11.4) with two unknowns and therefore a
solution may be found.
4.7 At the outset it was assumed that the firm would default when its total market value
reaches the book value of its liabilities, based upon empirical analysis of defaults, does still
assumption still hold?
KMV determines the percentage drop in the firm value that would bring it to default point. For
instance, if the firm’s expected value in one year was 100, and its default point was 25, then a 75
% drop in the asset value would bring it to the default point. The likelihood of a 75% drop
depends upon the volatility of the firm. By dividing the percentage drop by the volatility, KMV

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controls for the effect of different volatilities. Thus, if the firm’s volatility were 15% per year,
then a 75% drop would correspond to a five standard deviation event (75/15).
4.8 In view of KMV mechanics, how would you define distance to default?
The number of standard deviations that the asset value must drop in order to reach the default
point is called the distance to default, mathematically expressed as:
Expected market value of asset −default point
( Expected market value of assets ) ¿ ¿

4.9 Distance from default is an ordinal measure, akin to a bond rating. It still does not
tell you what the default probability is. How does KMV extend this risk measure to a
cardinal or a probability measure?
KMV uses historical default experience to determine an expected default frequency as a function
of distance from default. It does this by comparing the calculated distances from default and the
observed actual default rate for the same group of firms. A smooth curve fitted to those data
yields the EDF as a function of the distance from default. The associative relationship between
the desired distance to default using stock price data outstanding on the one hand and the
observed default frequency on the other constitutes the empirical component of this model.

Q5: Since the EDF relies on market prices to predict defaults, how does KMV apply such
data to private firms?
KMV uses data from public firms to develop an estimation model for the market value of assets
and asset volatility. It updates the parameters for these models frequently, as a way of connecting
current market information to private firms. However, these models, must rely upon the private
firm’s reported characteristics and accounting data, which may not be as timely or accurate as
would be ideal.

The market value of the firm is modelled as shuttling between values, the operating value and the
liquidating value. Using the market value and volatility the EDF is estimated for the distance-
from-default ratios on the basis of the public firm default experience in a similar manner to that
described above. However, the mapping between distance to default and EDF is slightly different

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between the public and private models, due to the information lost in using estimated rather than
actual market data.

Q6: What is the difference between KMV and other approaches?

The EDF model has two fundamental differences with other approaches: it relies on the
information in equity prices; and, it does not try explicitly to be predictive. Whereas agency debt
ratings are based upon trying to forecast future events, there are no real future forecasts in the
EDF model. It simply looks at the current value of the firm relative forecasts in the EDF model.
It simply looks at the current value of the firm relative to its default point and historical
volatility. Thus, if it has predictive power, it is because the current value of the firm is a good
prediction of future values. Since this value is derived from the firm’s equity market, the EDF
model is totally dependent on stock prices for its information content.

The most distinguishing feature of the EDF measure is that it imposes such a direct connection
between market values and default probabilities. Historically, there is a close connection between
changes in EDF values for a given firm and changes in the equity value of the firm, a much
closer connection than exists for any extant statistical models. In KMV view, this is a desirable
feature, because it represents a translation of the information in equity prices into credit
information. The KMV approach, to a considerable extent, represents a change in paradigm from
accounting based approaches to market value based approaches.

Q7: How do you test the predictive ability of default models?

The simplest test is to compare a specific prediction with the actual outcome. The forecast error
calculated from ex ante value (estimate) and ex post value (realization) is the best test of
performance.

If the predicted value of default probability were 25% and the realization 35%, then the model
error would be 40% (35-25/25). If the predicted probability were 25% and the realized default
was 15%, then the error would still be 40% (25-15/25). However, an error of the first kind (not
anticipating failure) would cost many, many times more than that of the second kind

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(overoptimistic failure). It should be noted that the forecast error is calculated not by applying it
to a single form, but to a group of firms with similar values of default probability.

Q8: Evaluate KMV’s applications within the banking sector

At one end of the spectrum, some banks use a company’s EDF as one more piece of information
among the general sources it consults. Other institutions have formally added EDF values as
supplemental information to the traditional credit analysis. Others use EDF as way of assigning
internal risk ratings to their credits. Some use EDF as an early warning tool in the portfolio
review group to alert loan officers about changes in a company’s risk profile.

The EDF model represents an innovative approach to utilizing stock market information in the
valuation of debt. Banks can no longer ignore equity market information. They need to monitor
equity market valuations constantly and to interpret the implications for credit risk.

Q9: What is the difference between structural and reduced form models?
The derivation of asset value, which has always been at the core of KMV EDF and models that
value credit-risky assets using Merton’s construct of debt as option are called ‘structural’ models.
While structural models develop asset values using a casual relationship between asset value and
debt value, in the other class of competing models called ‘reduced form’ models the approach
used is to value risky assets taking the default process (or default intensity) as ‘given’; that is, as
exogenous. In this approach, the model considers an idealized world where investors behave in a
risk neutral fashion and the default probabilities take on values such that when the probability-
weighted future cash flows from a bond are discounted by the risk-free, the resulting present
value exactly equals the observed price.

WEEK 8:
HOW MUCH CREDIT IN CREDIT RISK MODELS (PART 1)
8.1 What is the bank’s motivation to allocate economic capital? Isn’t regulatory capital
sufficient to cover losses?
Banks are required by their regulatory authorities to allocate regulatory capital for
expected losses and economic capital for unexpected losses.

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8.2 Why are traditional methods employed to determine the probability of default for
corporate customers?
These traditional methods would consist of models similar to Altman z-score and
therefore require financial and other characteristics. Ultimately such scores would be
subjective since you will be comparing the z-scores to a benchmark.
8.3 Why are ‘vendor-supplied’ and ‘internally developed credit scoring models
employed predominantly for retail, small and medium sized enterprise customers?
(slide no.4)
Banks receive a significant amount of loan applications per day and therefore they
require systems to process the requests and communicate to the customers the decision of
the bank. One way to execute such a process is by designing models and systems either
internally or ‘off-the-shelf’. Therefore banks will be able to process efficiently and
consistently within the bank’s policies.

8.4 Define ‘Through the cycle’ and ‘Point-in-time’ and discuss their relationship with
respect to default probabilities. (slide no. 5)
TTC defines a scenario where the loan holder is going through a period of financial
distress and the worst case scenario is considered. For example evaluations of their
abilities to remain solvent through a business cycle including a severe stress event is
considered. PIT defines a scenario based on best available information about their credit
quality.

The PDs wrt PIT are more volatile than TTC, since the TTC scenario assumes that the
client is undergoing severe stress and therefore assumes the worst. Under the PIT,
information is constantly being processed and therefore the PDs are as volatile and the
rate of information being received.

8.5 Discuss and evaluate how the definition of default varies across institutions and
asset classes
Is it when a client misses a loan repayment, is it when the same customer breached a
restrictive covenant, or when a listed firm is delisted ??? The questions keep on going and

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 many a time it in not clear when did the client default. The default point varies when you
have a retail customer, a home owner or a listed firm. Therefore from a bank’s
perspective it is essential that the bank is consistent with its policies and follows them
through to create robust credit models.

8.6 Explain in your own words what is Loss Given default and how does it differ to PD?
The LGD is a measure of the expected loss that the bank will experience per unit of
exposure should its counterparty default and is expressed as a percentage. It is expressed
as a percentage as PD but differs with respect to ‘per unit of exposure’.

8.7 Exposure at Default is often deemed to be the total interest bearing liabilities as
reported on the balance sheet. Is it really that straight forward?
Is it the Market value of exposure just prior to default? Or, The market value of the
exposure just prior to default but assuming it were risk-free? EAD is usually defined as
outstanding balance sheet exposure and in some cases includes also undrawn
commitments and advised limits, including unconditional and immediately cancellable
lines of credit.

8.8 The shorter the maturity on the loan, the less the core credit risk. Expand on this
statement.
Banks can deny credit, raise prices or demand greater protection (in the form of collateral
or seniority) in the quest to limit future losses to customers whose financial conditions
have deteriorated.

8.9 In most banks why is it that the default of a single counterparty is unlikely to be a
drain on capital?
Rather it is a series or group of defaults that poses a threat. Correlation is the driver that
determines the propensity of defaults to cluster and hence is an important factor in
portfolio analysis. A key differentiator between credit risk models is in the description
and calibration of correlations.

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8.10 What is asset correlation and how does this impact on PD and firm size?
Asset correlation essentially indicates the degree of co-movement between the asset value
of one borrower and the asset value of another. Asset correlations also influence the
shape of the risk weight formulas. They are asset-class dependent because different
borrowers and/or asset classes show different degrees of dependency on the overall
economy.

8.11 Conceptually how do the structural and reduced-form models differ?

Merton’s structural model issues early warnings of default by allowing a gradual
diffusion of asset values to the default point )equal to the debt level). As a result, this
process implies that the PD steadily approaches zero as the time to maturity decreases – a
result not observed empirically in the credit spread term structures.

In contrast to Merton models, credit spreads that are more firmly rooted in practical
experience are obtained from reduced-form or intensity-based models. Hence, whilst
Merton’s structural approach models default as the result of a gradual deterioration in
asset values, intensity-based approaches model default as sudden, unexpected events.
These models estimate PDs that are more consistent with empirical observations even
though they do not specify the economic process leading to default. Instead, model
default is a point process in which defaults occur randomly with a probability determined
by the intensity or hazard rate. Intensity-based models decompose observed credit
spreads on defaultable debt, or credit default swaps (CDS), to determine the PD
(conditional on no default having occurred prior to a specified time) as well as the LGD.

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 WEEK 9:
DEFAULT RECOVERY RATES AND LGD IN CREDIT RISK
MODELLING AND PRACTICE
9.1 List the three variables affecting credit risk and discuss how they are measured.
The three variables are PD, LGD and EAD. PD is a %, LGD is also a % and LGD is a nominal
figure measured in absolute dollar terms, i.e. $x.

9.2 Discuss the traditional perspective with respect to the relationship between PD and
RR. Comment on the discrepancy between theory and empirical findings.
The traditional approach of credit pricing models tends to focus on the systematic risk
components of credit risk, as these are the only ones that attract risk premia. Furthermore, credit
risk models traditionally assumed RR to be dependent on individual features like for example
collateral and seniority. These factors do not respond to systematic factors and therefore are
independent of PD. Such traditional focus on default analysis has been partly reversed by the
recent increase in the number of studies between PD and RR. This is partly the consequence of
the parallel increase in default rates and decrease of RR registered during the 1999-2002 period.
More generally evidence from many countries in recent years suggest that collateral values and
RR can be volatile and moreover, they tend to go down just when the number of defaults goes up
in economic downturns.

9.3 Briefly outline the way credit risk models developed during the last 30 years and
comment on the developments within the first-generation models.
Credit risk models

Credit pricing models Portfolio credit value-

at-risk

- First-generation structural form

- Second generation structural form
- Reduced form models
First-generation models: Merton’s model (1974) used the principles of option pricing (Black and
Scholes, 1973). In such a framework the default process of a company is driven by the value of

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the company’s assets relative to its liabilities and the risk of a firm’s default is therefore
explicitly linked to the variability of the firm’s asset value. In addition to Marton, first generation
models include Black and Cox (1976), Geske (1977) and Vasicek (1984), among others. Each of
these models tries to refine the original Merton framework by removing one or more of the
unrealistic assumptions. Black and Cox introduce the possibility of more complex capital
structures, with subordinated debt. Geske (1977) introduces interest-paying debt. Vasicek (1984)
introduces the distinction between short and long term liabilities.

9.4 The Merton approach has been useful in addressing the qualitatively important
aspects of pricing credit risk, however it has been less successful in practical
applications. Discuss.
Under Merton’s model, the firm defaults only at maturity of the debt, a scenario that is at odds
with reality. For the model to be used in valuing default-risky debts of a firm with more than one
class of debt in its capital structure (complex capital structures), the priority/seniority structures
of various debts have to be specified. Also this framework assumes that the absolute priority
rules are actually adhered to upon default in that debts are paid off in the order of their seniority.
However, empirical evidence indicates that the absolute-priority rules are often violated. The use
of a lognormal distribution in the basic Merton model (instead of a fat-tailed distribution) tends
to overstate recovery rates in the event of default.

9.5 Why are second-generation models more accurate than the first?
In response to such difficulties, an alternative approach has been developed which still adopts the
original the original Merton framework as far as the default process is concerned but at the same
time removes one of the unrealistic assumptions of the Merton model. Namely that default can
occur only at maturity of the debt when the firm’s assets are no longer sufficient to cover debt
obligations. Instead, it is assumed that default may occur anytime between the issuance and
maturity of the debt and that default is triggered when the value of the firm’s assets reaches a
lower threshold level.

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Under these models, the RR in the event of default is exogenous and independent from the firm’s
asset value. It is generally defined as a fixed ratio of the outstanding debt value and is therefore
independent from the PD. Longstaff and Schwartz (1995) argue that by looking at the history of
defaults and the recovery rates for various classes of debt of comparable firms, one can form a
reliable estimate of the RR. In their model, they allow for a stochastic term structure of interest
rates and for some correlations between defaults and interest rates. They find that this correlation
between default risk and the interest rate has a significant effect on the properties of the credit
spread. This approach simplifies the first class of models by both exogenously specifying the
cash flows to risky debt in the event of bankruptcy and simplifying the bankruptcy process. The
latter occurs when the value of the firm’s underlying assets hits some exogenously specified
boundary.

9.6 Despite improvements with respect to the second generation models, they still suffer
from drawbacks. List and discuss these drawbacks.
There are three main drawbacks which represent the main reasons behind their relatively poor
empirical performance. (i) they still require estimates for the parameters of the firm’s asset value
which is nonobservable. Indeed, unlike the stock price B&S (Black and Scholes) formula for
valuing equity options, the current market value of a firm is not easily observable. (ii) structural-
form models cannot incorporate credit rating changes that occur quite frequently for default-risky
corporate debts. Most corporate bonds undergo credit downgrades before they actually default.
As a consequence, any credit risk model should take into account the uncertainty associated with
credit risk model should take into account the uncertainty associated with credit rating changes
as well as the uncertainty concerning default. (iii) Finally most structural-form models assume
that the value of the firm is continuous in time. As a result, the time of default can be predicted
just before it happens and hence as argued by Duffe and Lando (2000) there are no sudden
surprises. In other words, without recurring to a ‘jump process’, the PD of a firm is known with
certainty.

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9.7 Reduced-form models are an attempt to overcome the shortcomings of structural
models. Discuss
Unlike structural-form models, reduced-form models do not condition default on the value of the
firm, and parameters related to the firm’s value need not be estimated to implement them. In
addition, reduced-form models introduce separate explicit assumptions on the dynamic of both
PD and RR. These variables are modelled independently from the structural features of the firm,
its asset volatility and leverage. Generally speaking, reduced-form models assume an exogenous
RR that is independent from the PD and take as basics the behaviour of default-free interest
rates, the RR of defaultable bonds at default, as well as a stochastic process for default intensity.
At each instant, there is some probability that a firm default on its obligations. Both this
probability and the RR in the event of default may vary stochastically through time. Those
stochastic processes determine the price of credit risk. Although these processes are not formally
linked to the firm’s asset value, there is presumably some underlying relation. This Duffe and
Singleton (1999) describe these alternative approaches as reduced-form models. Furthermore,
reduced-form models fundamentally differ (i) from their typical structural-form models in the
degree of predictability, and (ii) by the manner in which the RR is parametrized, (iii) other
models assume that the bonds of the same issuer, seniority and face value have the same RR at
default regardless of the remaining maturity.

9.8 Why did Credit Value-At-Risk models become popular during the second half of the
1990s?
Banks and consultants started developing models aimed at measuring the potential loss, with a
predetermined confidence level, that a portfolio of credit exposures could suffer within a
specified time horizon (generally one year). These were motivated by the growing importance of
credit risk management especially since the now complete Basel 2 was anticipated to be
proposed by the BIS. These VAR models include JP Morgan CreditMetrics, Credit Suisse
Financial Products CreditRisk etc.

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9.9 Discuss these Credit VaR models and indicate why they are better than the previous
models.
Credit VaR models:

Default mode (DM) Mark-to-market (MTM)

Credit risk in DM models identifies default risk by a binomial approach. Therefore, only two
possible events are taken into account – default and survival. DM includes all possible changes
of the borrower creditworthiness, technically called credit migration. In DM models, credit
losses only arise when a default occurs. MTM models are multinomial, in that losses arise also
when negative credit migration occurs. The two approaches basically differ for the amount of
data necessary to feed them, limited in the case of default model models, much wider in the case
of MTM ones.

The main output of a credit risk model is the probability density function (PDF) of the future
losses on a credit portfolio. From the analysis of such a loss distribution, a financial institution
can estimate both the expected loss and the unexpected loss on its credit portfolio. The expected
loss equals the (unconditional ) mean of the loss distribution; it represents the amount the
investor can expect to lose within a specific period of time (usually one year). On the other side,
the unexpected loss represents the deviation from expected loss and measures the actual portfolio
risk. This can in turn be measured as the standard deviation of the loss distribution. Such a
measure is relevant only in the case of a normal distribution and is therefore hardly useful for
credit risk measurement indeed, the distribution of credit losses is usually highly asymmetrical
and fat-tailed. This implies that the probability of large losses is higher than the one associated
with a normal distribution. Financial institutions typically apply credit risk models to evaluate
the economic capital necessary to face the risk associated with their credit portfolios. Credit VaR
can largely be seen as reduced-form models where the RR is typically as an exogenous constant
parameter or a stochastic variable independent from PD.

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9.10 PD/default rates have an inverse relationship to recovery rates. Discuss this
statement in terms of Bakshi et al (2001), Jokivuolle and Peura (2003) and Frye
(200a and 2000b).
Bakshi enhanced the reduced-form to allow for a flexible correlation between the risk-free rate,
the DP and the RR. Based on some evidence published by rating agencies, they force RR to be
negatively associated with DP. They find some strong support for this through the analysis of a
simple BBB-rated corporate bonds. Jokivuolle and Peura present a model for bank loans in
which collateral value is correlated with the PD. They use the option pricing framework for
modelling risky debt; the borrowing firm’s total asset value triggers the RR. Rather, the collateral
value is in turn assumed to be the only stochastic element determining recovery. Because of this
assumption, the model can be implemented using an exogenous PD so that the firm’s value
parameters need not be estimated. In this respect, the model combines features of both structural-
form and reduced form. Assuming a positive correlation between a firm’s asset value and
collateral value, the authors obtain a similar result as Frye that realized default rates and RR have
an inverse relationship.

Frye argues that these models are driven by a single systematic factor – the state of the economy
rather than a multitude of correlation parameters. These models are based on the assumption that
the sane economic conditions that cause defaults to rise might cause RR to decline, i.e. that the
distribution of recovery is different in high-default periods from the low-default ones. Frye used
PD and RR depend on the state of the systematic factor. The correlation between these two
variables derives from their mutual dependence on the systematic factor.

9.11 Use figure 16.1 (on page 287) to discuss the coincident relationship between high-
yield bond defaults and RR
The clear negative relationship between default and RR is striking with periods of excess supply
of defaults relative to demand resulting in unusually low recoveries in years 1990 to 2002. In
2005 and 2006, which are part of an extremely low default cycle, show estimates which are far
below the actual results. The graph predicts an above average RR of about 56% in 2006. Instead,
the actual rate was 65.3% and the 2005 estimate estimates of about 45% compared to the actual
RR of over 61%. Either the model has performed poorly or the default market has been

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influenced by an unusual amount of excess credit liquidity. Altman argues that there was a type
of credit bubble that causes seemingly highly distressed firms to remain non-bankrupt, when in
more normal periods many of these firms would have defaulted. This in turn, produced an
abnormally low default rate and the huge liquidity from distressed debt investors bid up to the
prices of both existing and newly defaulted issues.

9.12 How does procyclicality impact RR?

Altman highlights the implications of their results for credit risk modelling and for the issue of
procylcicality of capital requirements. In order to assess the impact of a negative correlation
between default rates and RR on the credit risk models, they run Monte Carlo simulations on a
sample portfolio of bank loans and compare the key risk measures (expected and unexpected
losses). They show that both the EL and the UL are vastly understated if one assumes that PDs
and RRs are uncorrelated. Therefore, credit models do not carefully factor in the negative
correlation between PDs and RRs might lead to insufficient bank reserves and cause unnecessary
shocks to financial markets.

As far as pro is concerned, they show that this effect tends to be exhausted by the correlation
between PDs and RRs: low recovery rates when defaults are high would amplify cyclical effects.
This would especially be true under the so-called ‘advanced’ IRB, where the banks are free to
estimate their own recovery rates and might tend to revise them downwards when defaults
increase and ratings worsen. The impact of such a mechanism was also assessed by Resti (2002),
based on simulations over a 20-year period, using a standard portfolio of bank loans. Two main
results emerge; (i) the pro effect is driven more by up and downgrades, rather than by default
rates, adjustments in credit supply needed to comply with capital requirements respond mainly to
changes in the structure of weighted assets and only to a lesser extent to actual losses; (ii) when
RRs are permitted to fluctuate with default rates, the pro effect increases significantly.

WEEK 10:
CREDIT DERIVATIVE PRODUCTS

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10.1 Explain how the asset swap arbitrage works and provide an example using the
following instruments/rates:
5- year fixed bond rate of 6%
5-year FRN yield of LIBOR +35bps
5-year swap rate of LIBOR +50bps
The asset swap arbitrage works when an investor can create a synthetic floating-rate asset
through a combination of a fixed-rate bond and an interest rate swap at yield levels that are more
attractive than a straight investment in a floating-rate asset (or vice-versa in the case of a
synthetic fixed-rate asset).

In this example the investor can receive 6% by investing in the bond directly and can swap the
fixed coupon for LIBOR flat in the swap market at a level of 5.50%; this allows it to create a
synthetic floating-rate asset at a gross pickup of 50bps. If it were to buy the FRN directly in the
market and fund at LIBOR flat, it would earn 35bps running; the synthetic asset swap arbitrage
therefore yields an incremental yield of 15bps running.

10.2 Describe how a bank or investor can obtain default protection by using as asset
swap switch.
An investor can contract to switch out of an asset swap package of a weaker credit reference in
exchange for that of a stronger reference. As the weaker reference deteriorates into a state of
financial distress, the investor has an effective put to its switch counterparty; in the extreme, as
the reference defaults, the switch counterparty is obliged to accept the defaulted package.
Naturally, the investor may have to pay a significant premium for this type of switch protection.

10.3 In what way is a CDS different to a conventional OTC swap contract? Describe a
more appropriate analogy from the financial markets.
A conventional OTC swap is a bilateral contract that calls for the exchange of periodic flows on
a two-way basis. A CDS is not a swap in the conventional sense: it is a unilateral contract that
involves only the contingent payment of a single flow if default occurs. The CDS is much closer
in structure and function to a default option, which is a unilateral, single payment contract.

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10.4 Name three factors that drive the price of a CDS and describe how each one
influences prices levels.
The price of the CDS is influenced by the probability that the reference credit will default (the
greater the probability, the higher the CDS price), the expected recovery rate (the higher the
recovery rate, the lower the CDS price), and the correlation between the creditworthiness of the
CDS counterparty and the reference credit (the higher the correlation, the lower the CDS price).

10.5 Explain why an unfunded TRS is similar to a synthetic financing

The total return receiver in an unfunded TRS uses no cash either to collateralize the transaction
or purchase a securities portfolio (for the LIBOR stream), yet it obtains the economics of the
reference security as if it had borrowed to purchase it; the LIBOR stream payable to the total
return is akin to the financing cost on the transaction.

10.6 If an investor buys a 12-month credit spread call option on Company ABC’s bond
with a strike spread of 100bps for a premium of 35 bps, what is the appropriate course of
action if ABC’s spread tightens to 50bps? Widens to 150bps? What is the breakeven level
of the trade?
If the spread tightens to 50 bps, the investor should exercise the option for a net gain of 15bps
(eg 100 bps strike – 50 bps market – 35 bps premium) and a dollar equivalent gain of 15bps
*notional*duration. If it widens, the investor must allow it to expire unexercised, as the option is
out-of-the-money. The breakdown level on the trade occurs at a spread level of 65 bps (eg 100
bps strike – 35 bps premium);each 1 bp tightening after 65 bps generates profit.

10.7
Assume the following reference credit portfolio:
Credit 1: $10 million notional, postdefault price 40
Credit 2: $10 million notional, postdefault price 30
Credit 3: $10 million notional, postdefault price 50
Given a $30 million structure, how much will an investor receive?
(a) If credit 2 defaults in a standard default?
The investor will receive $7 million, which is simply $10mn *(1-0.30)

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(b) If credit 2 defaults in a first-to-default basket?

The investor will still receive $7 million, as only one credit has defaulted

(c) If credit 1 and 2 default in a first-to-default basket (in that order)?

The investor will receive $6 mn, which is $10mn *(1-0.40) for the first credit to default;
the transaction then terminates, meaning no payment is due the investor on the second
credit default.
(d) If credit 3 defaults in a senior basket with a $5 mn first-loss limit?
The investor will receive no payout; the payout on a standard basket would be $5mn
($10mn*(1-0.50)), but the loss limit on the senior basket is set at $5mn.
(e) If credit 1 defaults in a senior basket with a $5 mn first-loss limit?
The investor will receive a $1mn payout; the payout on a standard basket for credit 1 is
$6mn ($10mn *(1-0.40)) and the loss limit is $5mn, indicating a net payment of $1mn.

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