7.1

Front 1

Ratings Migration

Back 1

is a positive or negative change in credit rating

Front 2

Structural models

Back 2

*way of modeling credit risk a
Structural models explicitly take into account various underlying factors that drive the default process, such
1. behavior of the underlying assets, and
2. the structuring of the cash flows (i.e., debt level)

Front 3

Reduced form models

Back 3

in contrast to structural models do not attempt to look at the strcutur reasons for default. Reduced form models take default or, more generally, ratings changes as events that take place with a particular probability and attempt to model this probability and insert the probability into a ricing equation.

Front 4

Arbitrage free model

Back 4

* a model for credit risk
8 an ideal credit risk model should be arbitrage-free, viz, the relationships expressed by teh model should be based on the assumption that arbitrage oppportunities cannot and do not persists.
* an arbitrage free model generates prices adn price relationship that do not allow any market participant with any methodology to earn consistent riskless profits above the riskless rate. Put differently, an arbitrage-free model specifies the prices that must relate to each other such that there will be no arbitrage opportunities.

Front 5

Steps in constructing arbitrage-free credit models

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1. construct a framework of possible interest rates and credit spreads, derived from a historical or simulated distribution, and
2. fit the parameters of that framework to the market prices of bonds that are deemed to be reliable (i.e., that are traded in highly competitive markets.

Front 6

Advantages of structural models

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* fixed-income securities can be priced using equity market data, which is reliable and easily obtainable
* structural models explain default based on fundamentals of the debt issuer (e.g., balance sheet position, market value of assets), which are often readily available
* the model is flexible enough to price related fixed-income securities such as convertibles or different seniority issues
* modeling default correlation is straightforward

Front 7

Disadvantages of structural models

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* distortion in equity prices will misprice fixed-income securities
* computed credit spreads from Merton's model are too low for ver short term and very high quality debt. Extensions of the model correct this irregularity but add more complexity to estimation procedure.
* the arbitrage-free assumes the entire firm's assets are tradable adn can be hedged, which may not be the case
* Data on firm liabilities may be unavailable due to an issuer's lack of transparency and accounting choices
* economic behavior of the firm may change as the firm approaches default, which makes modeling problematic
* financial institutions are regulated and so their default threshold may not be the point at which the asset value is less than the value of the liabilities
* the added complexity of sovereign issues not captured in structural models

Front 8

Expected credit loss

Back 8

PD * EAD * (1-R)

PD = probability of default
EAD = exposure at default
LGD = loss given default

Front 9

Advantages of the reduced-form model

Back 9

* the model incorporates the fixed-income market's assessment of default, which is inferred from bond prices (i.e., yields) and credit default swaps
* the model is very user friendly and can price derivatives and portfolios quite easily
* the model can adjust for credit ratings changes
* the model can be used when balance sheet information is not available (e.g., sovereign debts)

Front 10

Disadvantages of the reduced-form model

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* The model is sensitive to key assumptions (e.g., recovery rate)
* Reduced-form models do not provide much information about the fixed-income instruments used in model construction
* In contrast to interest rate data and models, there are very limited observations to help guide proper default probability rates, which use hazard models

Front 11

attachment point

Back 11

An attachment point or lower attachment point is the minimum percentage loss in CDO collateral that will begin to reduce the value of a tranche. A detachment point or upper attachment point is the percentage loss that would result in total loss of a tranche's value

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V(t)

Back 12

current market value of the firm's assets

Front 13

B(t, T)

Back 13

the current value of debt at time t, and a maturity date of T

Front 14

S(t)

Back 14

current market value of equity

Front 15

P(K, t, T)

Back 15

The current price of a European put option on the firm's assets with the exercise price of K and maturity take of T

Front 16

Risk-neutral probabilities

Back 16

Risk-neutral probabilities are those statistical probabilities that if used would correctly give the fair price of a security under the assumption that investors are risk-neutral.

Front 17

Black-Scholes

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- models option prices assuming continuous-time trading and allowing an infinite number of outcomes by assuming that asset returns are lognoramally distributed. So the BS model provides a more realistic portrayal of asset price movements than the single-period binomial model