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##### Subject 3. Structural and Reduced Form Credit Models
In general there are two categories in credit analysis models: structural models and reduced-form models.

Structural Models

Structural models are based on the structure of a company's balance sheet.

The Option Analogy

Assume a zero-coupon bond with a face value of K matures at time T. The time T value of a company's assets is AT.

Owning the company's equity = Owning a European call option on the company's assets, with strike price K and maturity T.

At time T, the equity owners will:

• Pay K to debt-holders and keep AT - K, if AT >= K, or
• Default, if AT < K.

This implies that:

• Probability of default at time T = Probability of decrease in asset's value below K.
• The loss given default = K - AT.

Debt Option Analogy

Owning the company's debt = Owning a riskless bond that pays K with certainty at time T, and simultaneously selling a European put option with strike price K.

Value of risky debt = Value of riskless debt - Put option's price

Main strength: It provides useful economic intuition to understand a company's default probability and recovery rate.

Weaknesses: The default probability and recovery rate depend crucially on the assumed balance sheet of the company and its liability structure. However, a company's asset value is usually not observable.

Reduced-Form Models

The models assume:

• A company defaults at a random time t. The default time can be modeled., and the default probability explicitly depends on the business cycle.
• Given the vector of macroeconomic state variables Xt, a company's default represents idiosyncratic risk. This means whether a particular company defaults depends only on company-specific considerations.
• The company's default probability does not explicitly depend on the company's balance sheet. In the event of default, reduced form models allow the company's different liabilities to have different loss rates.

Strengths:

• Historical estimation method can be used because both the economy's macroeconomic variables and the company's debt prices are observable.
• The credit risk measures reflect changing business cycle.
• The company's probability of default does not explicitly depend on the company's balance sheet.

Main weakness: the models do not explain the economic reasons for default. They assume default comes as a "surprise" and can occur at any time, which is not true in reality.

The choice of credit risk model depends on how it is to be used and by whom.

• Structural models require information best known to the managers of the company. They can be used for internal risk management, banks' internal credit risk measures, and for publicly available credit ratings.
• Reduced-form models require information generally available in financial markets. They should be used to value debt securities and credit derivatives.

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