The Black Scholes Model and Its 4 Important Advantages

Are you looking for what the Black Scholes Model is? AAMcourses is here to help you finish your search. In this article, we will discuss what the Black Scholes Model is, how it works, its formula, assumptions, limitations, and advantages of the model.

The Black Scholes or the Black Scholes-Merton is a financial model used whose formula is used to forecast the prices of options – Call and Put. The Black Scholes model was first introduced to the European market for estimating option prices. Before that, the world did not have a model that would help forecast options prices. It has been researched that no model has given results as well as the Black Scholes Model, the result of this model are closest to the actual price fluctuations.

The model was founded by Fischer Black and Myron Scholes at first, after the contribution of Robert Merton; the Model was said as the Black-Scholes-Merton Model. In 1997, Myron Scholes and Robert Merton received the Economist Nobel Prize. Fischer Black was named the contributor even though he had passed away during that time.

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Let’s study in detail the Black Scholes Model.

The Black Scholes Model

The Black Scholes Model is a mathematical model used for pricing financial derivatives. The model can only be used for non-dividend-paying derivatives. The model estimates the theoretical value of the derivatives based on six variables. These variables are :

• Volatility
• Type
• Underlying Asset Price
• Strike Price
• Time
• Risk-Free Rate

The Black Scholes Model was developed in 1973 by Fischer Black, Myron Scholes, and Robert Merton. One of the critical assumptions of the Black Scholes Model is that an option’s price is different despite the risk of the underlying asset and expected return. The model is based on the concept of hedging and removes the risk associated with the volatility of the underlying asset.

The original Black Scholes Model can only be used for pricing European derivatives. The main difference between European and American options is that the European option can be practiced only at its expiry date. In contrast, in the case of American options, they can be practiced at any time till the expiry date.

The Formula for the Black Scholes Model

At first glance, the formula for the Black Scholes Model is quite challenging. But we live in an internet-operated generation with several calculators that help us in the process. The formula for the model is given below.

Where,
C = Call option price
S = Current stock price
K = Strike price
r = Risk-free interest rate
t = Time of maturity
N = Normal distribution

Assumptions of the Black Scholes Model

1. Volatility: One of the model’s assumptions is that the volatility remains constant throughout the option’s life till maturity. 
2. Lognormal Distribution: The model assumes that the price of the underlying asset follows a lognormal distribution based on the principle that the price of the underlying asset cannot be negative. 
3. No Dividends: The model assumes that underlying assets do not pay dividends. 
4. Practiced on Maturity: The model assumes that options can only be practiced on maturity. 
5. Risk-free Interest rate: The model assumes that the risk-free interest rate remains constant throughout the option’s life. 
6. Frictionless Market: The model assumes no transaction costs such as brokerage and commissions.
7. Random Walk: The model assumes that the market fluctuations are random and have no basis. 

Limitations of the Black Scholes Model

• The model can only be used to price the European option because it only considers the maturity date. The model is useless for American options as they can be practiced anytime before maturity.
• The model assumes that the volatility remains constant till the maturity date, but the volatility keeps fluctuating.
• The model also assumes that the risk-free interest rate remains constant throughout the option’s life, i.e., till the maturity date.
• The model assumes there is no transaction fee, which is not possible in the market.
• The model assumes that the price fluctuations are completely random, but research shows that fluctuations tend to keep going up in the intermediate terms and vice versa.

Advantages of the Black Scholes Model

High Accuracy

The Black Scholes Model is one of the most accurate option pricing models. It considers all six variables – Volatility, Type, Underlying Asset Price, Strike Price, Time, and Risk-Free Rate which help the results be more accurate.

Quick Calculations

The model can calculate large amounts of data faster than other models with high accuracy. Other models are more accurate but take a long time to calculate the prices.

Flexible to the Market

The Black Scholes Model offers not only quick and accurate calculation for option pricing but also other market instruments such as bonds.

Analyses Volatility of the Underlying Assets

The Model helps to understand the volatility of the underlying assets. This allows the investor to minimize the risk from asset volatility even though the model assumes that volatility is constant. This helps investors to analyze whether the market is profitable or not.

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FAQs

Closing Statement 

The Black Scholes Model is the best alternative for calculating option prices. The model provides a straightforward way of calculating option prices. New and modified model versions have been created to suit markets other than the European market. Even though the model has several unrealistic assumptions, the Black Scholes Model is still the best alternative for calculating option prices.

I hope this article about the Black Scholes Model is informative. If you have any doubts or suggestions, practice them in the comment box.