## What is the 'Merton Model'

The Merton model is an analysis model – named after economist Robert C. Merton – that is used to assess the credit risk of a company's debt. Analysts at brokerage firms and investors utilize the Merton model to understand how capable a company is at meeting financial obligations, servicing its debt and weighing the general possibility that the company will go into credit default. This model was later built out by Fischer Black and Myron Scholes to develop the Black-Scholes pricing model.

Next Up

## BREAKING DOWN 'Merton Model'

Loan officers and stocks analysts utilize the Merton model to analyze a corporation's risk of credit default. This model allows for easier valuation of the company and also helps analysts determine if the company will be able to retain solvency by analyzing maturity dates and debt totals.

## The Black-Scholes Model and the Merton Model

Merton purchased his first stock at age 10 and eventually went to MIT for graduate work. There, he developed and published groundbreaking and precedent-setting ideas to be utilized in the financial world.

Black and Scholes, during Merton’s time at MIT, developed a critical insight that by hedging an option, systematic risk is removed. Merton then developed a derivative showing that hedging an option would remove all risk. In their 1973 paper, "The Pricing of Options and Corporate Liabilities," Black and Scholes included Merton's report, which explained the derivative of the formula. Merton changed the name of the formula to the Black-Scholes model because he felt it would be pretentious to name something after oneself.

## Understanding the Model

The Merton (or Black-Scholes) model calculates theoretical pricing of European put and call options without considering dividends paid out during the life of the option. The model can, however, be adapted to consider these dividends by calculating the ex-dividend date value of underlying stocks.

The Merton model makes basic assumptions: all options are European and are exercised only at the time of expiration; no dividends are paid out; market movements are unpredictable (efficient markets); no commissions; underlying stocks' volatility and risk-free rate are constant; returns on underlying stocks are regularly distributed. Variables that were taken into consideration in the formula include options strike price, present underlying price, risk-free interest rates and the amount of time before expiration.

The formula for the model is: C = SN(d1)-Ke(-rt)N(d2), where C = Theoretical call premium, S = Current stock price, t = time, K = option striking price, r = risk free interest rate, N = Cumulative standard normal distribution, e = exponential term (2.7183), d1 = ( ln(S/K) + (r + (s2/2))t ) / s_t, d2 = d1 - s_t, s = standard deviation of stock returns. Consider a company's shares sell for \$210.59, stock price volatility is 14.04%, the interest rate is 0.2175%, the strike price is \$205 and expiration time is four days. With the given values, the theoretical call option is negative 8.13.

RELATED TERMS
1. ### Robert C. Merton

Robert C. Merton is a Nobel Prize-winning economist renowned ...
2. ### Myron S. Scholes

Nobel Prize winning economist Myron Scholes is as famous for ...
3. ### Option Pricing Theory

An option pricing theory is any model or theory-based approach ...
4. ### William F. Sharpe

William F. Sharpe is an American economist who won the 1990 Nobel ...
5. ### Lattice-Based Model

A lattice-based model is a model used to value derivatives; it ...
6. ### Default Model

Default model is constructed by financial institutions to determine ...
Related Articles
1. Investing

### Understanding the Black-Scholes Model

The Black-Scholes model is a mathematical model of a financial market. From it, the Black-Scholes formula was derived. The introduction of the formula in 1973 by three economists led to rapid ...

### The Anatomy of Options

Find out how you can use the "Greeks" to guide your options trading strategy and help balance your portfolio.

### Understanding How Dividends Affect Option Prices

Learn how the distribution of dividends on stocks impacts the price of call and put options, and understand how the ex-dividend date affects options.

### Breaking Down The Binomial Model To Value An Option

Find out how to carve your way into this valuation model niche.
5. Investing

### What's the Gordon Growth Model?

The Gordon growth model is used to calculate the intrinsic value of a stock today, based on the stock’s expected future dividends. It is widely used by investors and analysts to compare the predicted ...

RELATED FAQS
1. ### What is the difference between financial forecasting and financial modeling?

Understand the difference between financial forecasting and financial modeling, and learn why a company should conduct both ... Read Answer >>
2. ### How can derivatives be used to earn income?

Learn how option selling strategies can be used to collect premium amounts as income, and understand how selling covered ... Read Answer >>
Hot Definitions
1. ### Gross Margin

A company's total sales revenue minus its cost of goods sold, divided by the total sales revenue, expressed as a percentage. ...
2. ### Inflation

Inflation is the rate at which prices for goods and services is rising and the worth of currency is dropping.
3. ### Discount Rate

Discount rate is the interest rate charged to commercial banks and other depository institutions for loans received from ...
4. ### Economies of Scale

Economies of scale refer to reduced costs per unit that arise from increased total output of a product. For example, a larger ...
5. ### Quick Ratio

The quick ratio measures a company’s ability to meet its short-term obligations with its most liquid assets.
6. ### Leverage

Leverage results from using borrowed capital as a source of funding when investing to expand the firm's asset base and generate ...