Merton Model

What Is the Merton Model?

The Merton model is an analysis model used to evaluate the credit risk of a company's debt. Analysts and investors use the Merton model to comprehend how capable a company is at meeting financial obligations, servicing its debt, and gauging the overall possibility that it will go into credit default.

In 1974, economist Robert C. Merton proposed this model for evaluating the structural credit risk of a company by modeling the company's equity as a call option on its assets. This model was subsequently extended by Fischer Black and Myron Scholes to foster the Nobel-prize winning Black-Scholes pricing model for options.

The Formula for the Merton Model Is

$\begin &E=V_tN\left(d_1\right)-Ke^{-r\Delta}N\left(d_2\right)\ &\textbf\ &d_1=\frac{\ln{\frac}+\left(r+\frac{\sigma_v^2}{2}\right)\Delta}{\sigma_v\sqrt{\Delta}}\ &\text\ &d_2=d_1-\sigma_v\sqrt{\Delta}\ &\text{E = Theoretical value of a company's equity}\ &V_t=\text{Value of the company's assets in period t}\ &\text{K = Value of the company's debt}\ &\text\ &\text\ &\text\ &\text\ &\text\left(i.e. \text2.7183...\right)\ &\sigma=\text\ \end$

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 the expiration time is four days. With the given values, the theoretical call option value created by the model is - 8.13.

What Does the Merton Model Tell You?

Loan officers and stock analysts use the Merton model to dissect an organization's risk of credit default. This model takes into account simpler valuation of the company and furthermore assists analysts with deciding whether the company will actually want to hold solvency by breaking down maturity dates and debt sums.

The Merton (or Black-Scholes) model calculates the theoretical pricing of European put and call options disregarding dividends paid out during the life of the option. The model can, notwithstanding, be adjusted to consider these dividends by calculating the ex-dividend date value of underlying stocks.

The Merton Model makes the accompanying essential presumptions:

• All options are European and are exercised exclusively at the hour of expiration.
• No dividends are paid out.
• Market developments are unpredictable (efficient markets).
• No commissions are incorporated.
• Underlying stocks' volatility and risk-free rates are consistent.
• Returns on underlying stocks are consistently distributed.

Variables that were thought about in the formula incorporate options strike prices, present underlying prices, risk-free interest rates, and the amount of time before expiration.

The Black-Scholes Model Versus the Merton Model

Robert C. Merton was a renowned American economist and Nobel Memorial Prize laureate, who befittingly purchased his most memorable stock at age 10. Afterward, he earned a Bachelor in Science at Columbia University, a Masters of Science at California Institute of Technology (Cal Tech), and a doctorate in economics at Massachusetts Institute of Technology (MIT), where he later become a teacher until 1988. At MIT, he developed and distributed noteworthy and point of reference setting thoughts to be used in the financial world.

Black and Scholes, during Merton's time at MIT, developed a critical knowledge that by hedging an option, systematic risk is eliminated. Merton then developed a derivative appearance that hedging an option would eliminate all risk. In their 1973 paper, "The Pricing of Options and Corporate Liabilities," Black and Scholes incorporated Merton's report, which explained the derivative of the formula. Merton later changed the name of the formula to the Black-Scholes model.

Features

• The Merton model gives a structural relationship between the default risk and the assets of a company.
• This method considers the utilization of the Black-Scholes-Merton option pricing model.
• In 1974, Robert Merton proposed a model for surveying the credit risk of a company by modeling the company's equity as a call option on its assets.