Definicja modelu Mertona
Co to jest model Mertona?
Model Mertona jest modelem analitycznym używanym do oceny ryzyka kredytowego zadłużenia przedsiębiorstwa. Analitycy i inwestorzy wykorzystują model Mertona, aby zrozumieć, jak zdolna jest firma do wywiązywania się ze zobowiązań finansowych, obsługi zadłużenia i rozważenia ogólnej możliwości, że popadnie w niespłacanie kredytu.
W 1974 r. Ekonomista Robert C. Merton zaproponował ten model oceny strukturalnego ryzyka kredytowego przedsiębiorstwa, modelując kapitał własny przedsiębiorstwa jako opcję kupna na jego aktywa. Model ten został później rozszerzony przez Fischera Blacka i Myrona Scholesa w celu opracowania nagrodzonego Noblem modelu wyceny Black-Scholesa dla opcji.
Wzór na model Mertona to
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 produced by the model is -8.13.
What Does the Merton Model Tell You?
Loan officers and stock 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 Merton (or Black-Scholes) 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 these dividends by calculating the ex-dividend date value of underlying stocks.
The Merton Model makes the following 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 are included.
- Underlying stocks’ volatility and risk-free rates are constant.
- Returns on underlying stocks are regularly distributed.
Variables that were taken into consideration in the formula include options strike prices, present underlying prices, risk-free interest rates, and the amount of time before expiration.
Key Takeaways
- In 1974, Robert Merton proposed a model for assessing the credit risk of a company by modeling the company’s equity as a call option on its assets.
- This method allows for the use of the Black-Scholes-Merton option pricing model.
- The Merton model provides a structural relationship between the default risk and the assets of a company.
The Black-Scholes Model Versus the Merton Model
Robert C. Merton was a famed American economist and Nobel Memorial Prize laureate, who befittingly purchased his first stock at age 10. Later, 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 professor until 1988. At MIT, 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 later changed the name of the formula to the Black-Scholes model.