**Structural Model**

Structural models of credit risk are based on issuer balance sheets and option pricing theory.

The oft-given analogy is that owning risky debt is equivalent to owning a risk-free bond and writing a European put option on the assets of the company. Owning equity in a company with risky debt is equivalent to owning a call option on company assets.

This is based on the upside and downside of bankruptcy vs profitability conditions of a firm.

A weakness of structural models is that they assume that company assets trade in a frictionless market with a mean return and variance condition. Other assumptions include that the risk-free rate is constant, and that the firm only has a single issue of risky debt. (Simple balance sheet)

Another limitation of the structural model is that estimations are needed to be made for the input parameters of the structural mode.

**Reduced Form Model**

Reduced form models are based on real work conditions using historical data for inputs. These models do not rely on assumptions on the treatment of a company’s balance sheet.

Reduced form models do assume that the company has at least one issue of risky zero coupon debt outstanding, but the risk-free rate, probability of default and recovery are based of the state of the economy.

Allowing the use of historical data is a strength, however this means that reduced form models must be properly backtested.