# Merton Model: Credit Risk Formula, History, and Insights Explained

![Merton Model](https://www.investopedia.com/thmb/Tjohp8maSJ7d2-4B4Q7dy_b_WKc=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/mertonmodel-final-fe302a90c73d4ed2b4e462ecb3a55119.png)

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## What Is the Merton Model?

The Merton Model, proposed by economist Robert C. Merton in 1974, is a vital tool for evaluating a company's credit default risk. By modeling corporate [equity](https://www.investopedia.com/terms/e/equity.asp) as a call option on its assets, it assists stock analysts and commercial loan officers in making informed decisions. Understanding the Merton Model provides insights into assessing structural [credit risk](https://www.investopedia.com/terms/c/creditrisk.asp) and supports better financial decision-making.

### Key Takeaways

*   The Merton model assesses a company's credit risk by modeling its equity as a call option on its assets.
*   Developed by Robert C. Merton in 1974, the model uses formulas to gauge the likelihood of credit default.
*   The Merton model relies on several assumptions, including that all options are European and no dividends are paid.
*   Robert C. Merton, along with Myron S. Scholes, received a Nobel Prize for their contributions to financial economics.

## How to Calculate the Merton Model Formula

$\begin{aligned} &E=V_tN\left(d_1\right)-Ke^{-r\Delta{T}}N\left(d_2\right)\\ &\textbf{where:}\\ &d_1=\frac{\ln{\frac{V_t}{K}}+\left(r+\frac{\sigma_v^2}{2}\right)\Delta{T}}{\sigma_v\sqrt{\Delta{T}}}\\ &\text{and}\\ &d_2=d_1-\sigma_v\sqrt{\Delta{t}}\\ &\text{E = Theoretical value of a company's equity}\\ &V_t=\text{Value of the company's assets in period t}\\ &\text{K = Value of the company's debt}\\ &\text{t = Current time period}\\ &\text{T = Future time period}\\ &\text{r = Risk-free interest rate}\\ &\text{N = Cumulative standard normal distribution}\\ &\text{e = Exponential term}\left(i.e. \text{ }2.7183...\right)\\ &\sigma=\text{Standard deviation of stock returns}\\ \end{aligned}$

## Insights From the Merton Model: What It Reveals

The Merton model helps analysts [value a company](https://www.investopedia.com/terms/v/valuation.asp) and determine its [solvency](https://www.investopedia.com/terms/s/solvency.asp) by analyzing debt [maturity dates](https://www.investopedia.com/terms/m/maturitydate.asp) and [debt](https://www.investopedia.com/terms/d/debt.asp) totals.

The Merton model calculates the theoretical prices for European [put](https://www.investopedia.com/terms/p/putoption.asp) and [call options](https://www.investopedia.com/terms/c/calloption.asp), not factoring in any dividends. The model can adjust for dividends by calculating the [ex-dividend](https://www.investopedia.com/terms/e/ex-dividend.asp) date of stocks.

The Merton model makes the following basic assumptions:

*   All options are [European options](https://www.investopedia.com/terms/e/europeanoption.asp) and are exercised only at the time of expiration.
*   No dividends are paid out.
*   Market movements are unpredictable (efficient markets).
*   No commissions are included.
*   Underlying stocks’ volatility and risk-free rates are constant.
*   Returns on underlying stocks are regularly distributed.

Variables that are taken into consideration in the formula include options’ [strike prices](https://www.investopedia.com/terms/s/strikeprice.asp), present underlying prices, risk-free interest rates, and the amount of time before expiration.

## The Evolution and Impact of the Merton Model 

[Robert C. Merton](https://www.investopedia.com/terms/r/robert-c-merton.asp) is an American economist who won the Nobel Prize and bought his first stock at 10. He studied engineering at Columbia University, got a master's in applied math at Caltech, and earned a PhD in economics from MIT, where he also taught.

At MIT, Merton worked with economists Fischer Black and Myron S. Scholes on [option](https://www.investopedia.com/terms/o/option.asp) pricing problems, helping each other with their research. Black and Scholes published a seminal paper on the topic, “The Pricing of Options and Corporate Liabilities,” in 1973. Merton’s “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” published early the following year, described what has come to be known as the Merton model.

In 1997, Merton and Scholes received the Nobel Prize for their groundbreaking formula for valuing stock options. The committee praised their work for advancing economic valuation, creating new financial tools, and improving risk management.”

Their best-known collaboration is often referred to today as the [Black-Scholes-Merton model](https://www.investopedia.com/terms/b/blackscholes.asp).

## What Is a Call Option?

A call option is a contract that allows the buyer to purchase a stock or other financial asset at a specified price by or on a certain date.

## What Is the Difference Between European and American Options?

European options can be [exercised](https://www.investopedia.com/terms/e/exercise.asp) only on their [expiration date](https://www.investopedia.com/terms/e/expirationdate.asp), while American options can be exercised anytime.

## What Is a Risk-free Interest Rate?

A [risk-free interest rate](https://www.investopedia.com/terms/r/risk-freerate.asp) is the theoretical rate of return on an investment carrying zero risk. It is theoretical because no investment is entirely without risk, although some come closer than others.

## The Bottom Line

The Merton model is a critical tool for assessing corporate credit risk, modeling a company's equity similar to a call option on its assets. Established by economist Robert C. Merton in 1974, this model aids stock analysts and loan officers in predicting a company's potential for credit default. While it simplifies understanding of a firm's creditworthiness, it operates under assumptions such as market efficiency and constant volatility, which users should consider when applying the model.

> **Article Sources**
>
> 1.  Massachusetts Institute of Technology, Sloan School of Management. “[Robert C. Merton](https://mitsloan.mit.edu/faculty/directory/robert-c-merton).”
>     
> 2.  The University of Chicago Press: Journals. “[The Pricing of Options and Corporate Liabilities](https://www.journals.uchicago.edu/doi/10.1086/260062).”
>     
> 3.  The Journal of Finance, via Wiley Online Library. “[On the Pricing of Corporate Debt: The Risk Structure of Interest Rates](https://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1974.tb03058.x).”
>     
> 4.  Journal of Economic Perspectives, via American Economic Association. “[In Honor of the Nobel Laureates Robert C. Merton and Myron S. Scholes: A Partial Differential Equation That Changed the World](https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.13.4.229).”