Merton Model
The Merton model is a mathematical formula that stock analysts and commercial loan officers, among others, can use to judge a corporation’s risk of credit default. Named for economist Robert C. Merton, who proposed it in 1974, the Merton model assesses the structural credit risk of a company by modeling its equity as a call option on its assets.
Definition: The Merton model is a mathematical formula used by stock analysts and commercial loan officers to assess the risk of a company's credit default. Proposed by economist Robert Merton in 1974, the model evaluates a company's structural credit risk by modeling the company's equity as a call option on its assets.
Origin: The origin of the Merton model dates back to 1974 when Robert Merton first introduced it in his paper. Merton's research was based on the Black-Scholes option pricing model and applied it to the analysis of corporate debt and equity. The introduction of this model marked a significant milestone in the field of credit risk assessment.
Categories and Characteristics: The Merton model is a type of structural credit risk model, characterized by: 1. Viewing a company's equity as a call option on its assets; 2. Assessing default risk through the company's asset value and liabilities; 3. Assuming the company's asset value follows a geometric Brownian motion. The model's advantages include a solid theoretical foundation and a clear method for calculating default probabilities, but its disadvantages are high sensitivity to input parameters and strict assumptions.
Specific Cases: Case 1: Company A has an asset value of $10 million and liabilities of $8 million, with an asset volatility of 20% and a risk-free rate of 5%. Using the Merton model, the company's default probability within one year can be calculated. Case 2: A bank uses the Merton model to assess the credit risk of its loan portfolio by analyzing the asset values and liabilities of various borrowing companies, determining the overall default risk level, and adjusting its lending strategy accordingly.
Common Questions: 1. The Merton model is highly sensitive to input parameters. How to choose appropriate parameters? Answer: Parameters can be estimated using historical data and market information, but attention must be paid to the model's assumptions. 2. The Merton model assumes that the company's asset value follows a geometric Brownian motion. Is this assumption reasonable? Answer: This assumption may not fully hold in practice, but it provides a certain simplification in theoretical analysis.
