Merton model & credit KMV

Credit risk modeling revolves around study to find out probability of default to consider credit risk that a firm is undertaking, Merton model act as foundation for majority of model being used to measure credit risk for any firm, another widely used model is credit KMV. KMV was developed by Moody, however it employs basic techniques of Merton model to find PD.

both models works on the basic assumptions -

• Brownian movement of stock price
  
• Perfect market scenario (Equity reflect true valuation of company assets)
  
• Equity volatility can be mapped to asset volatility

In Merton model , equity value of stock can be taken as call option on firm assets where strike price will be total debt of company. Let's go little deep in Merton model for option valuation-


N(d1) is the probability of stock price (S) ending more than (K) while N(d2) is the probability of same thing at risk neutral rate. N(d1)*S-N(d2)*K*exp(-r(T-t)) gives us the call option price and has been demonstrated by Black Sholes and is famous as BS formula.

As N(d1) represent probability of S being higher than K, Merton used same technique to find if company assets ends more than total debt. S was replaced by F (Firm Assets) and K was replaced by D (total debt). r was expected growth rate of assets and firm volatility was taken into account instead of equity volatility. There are number of techniques to find firm volatility , we can use following one

Volatility of Assets = Volatility of Equity * Equity value / Firm Value

Biggest disadvantage of Merton model was to assume default rate will follow normal probability as we putting d2 into N(d2) to default rate.

Credit KMV

Credit KMV came out with improvement on this instead of using normal distribution, they stopped at calculation of d2 and called it distance to default.Next step was to compare this value against database of historical US defaults to find probability of default, Moody has demonstrated (enron default) over time that KMV model is better than credit ratings as it quickly reflects the change in firm's position.