# Merton Model Definition History Formula What It Tells You

Merton Model: Definition, History, Formula, What It Tells You

What Is the Merton Model?

Key Takeaways

The Formula for the Merton Model

The Merton model allows for easier valuation of a company and helps analysts determine if it will be able to retain solvency, by analyzing the maturity dates of its debt and its debt totals.

The Merton model calculates the 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 dividends by calculating the ex-dividend date value of underlying stocks.

The Merton model makes the following basic assumptions:

– All options are European options 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, present underlying prices, risk-free interest rates, and the amount of time before expiration.

History of the Merton Model

During Merton’s time at MIT, he and fellow economists Fischer Black and Myron S. Scholes were all working on problems related to the pricing of options and often aided in each other’s work. 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.

Merton and Scholes were awarded the Nobel Prize for economics in 1997 (Black had died and was no longer eligible). The prize committee cited them for developing “a pioneering formula for the valuation of stock options. Their methodology has paved the way for economic valuations in many areas. It has also generated new types of financial instruments and facilitated more efficient risk management in society.”

Their best known collaboration is often referred to today as the Black-Scholes-Merton model.

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 only on their expiration date, while American options can be exercised at any time.

What is a risk-free interest rate?

A risk-free interest rate 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