Special models and formulas help investors to calculate realistic and fair prices. One useful model is the so-called Black Scholes model from 1973. In this article, you will find out exactly what the model can do, what it is used for and what advantages and disadvantages it offers.
Black Scholes model simply explained
With the help of this financial mathematical model, the Theoretical value of asset classes can be calculated. It is often used to Prices of derivatives and options to calculate. The model was developed back in 1973 by Fischer Black and Myron Scholes.
The model assumes that the market has at least one risky asset contains. This asset can be represented by a security such as a share, for example. In addition risk-free assets such as government bonds from countries with high credit ratings.
Different assumptions are made depending on whether the asset is risky or risk-free. In the case of a risky asset, it is assumed that the security does not pay dividends and that there are no risks. only one date of payment gives.
The risk-free asset is based on the assumption that money will be received at a constant interest rate can be lent or borrowed, shares without trading fee can be bought and sold and the market no arbitrage permitted.
Further assumptions of the model are:
- Taxes are not taken into account
- The market functions efficiently
- The base value moves according to a log-normal distribution
These assumptions are important as they result in the creation of hedged positions for call and put options in Europe. This involves a long position in a share and a short position in the option. The value of the option does not depend on the price of the share.
This background knowledge is important in order to understand how the price of options can be calculated using the model. The Black Scholes model contains a Formula for precise calculation.
Black Scholes model example
The model is useful for calculating the prices of options and derivatives. In addition, it can be used to check how changes in individual factors influence the price can.
The abbreviations and their meaning are shown in the table. These are important for understanding the actual formula:
| Abbreviation | Meaning |
| K | Exercise price |
| S0 | Current price of the underlying |
| r | Interest rate |
| t | Remaining term |
| N (d1) | Standard normal distribution of d1 |
| N (d2) | Standard normal distribution of d2 |
| d1 | [ln (S0 / K) + (r + σ2 / 2) × t] / (σ × sqrt (t)) |
| d2 | d1 - (σ × sqrt (t)) |
| σ | Volatility of the asset/underlying asset |
The formula of the Black Scholes model is as follows: Price = S0 × N (d1) - K × e-rt × N (d2)
Criticism of the Black Scholes model
A look at the basic assumptions of the model also reveals some points of criticism. For example, the model assumes risk-free, constant interest rates from what does not always correspond to reality.
Furthermore, it became clear that the model can only be used for Calculation of options within Europe can be applied. Options in America can be exercised before the expiry date, which is not taken into account in the model.
- It is also assumed that volatility remains the same during the term of the option, which is not the case in reality, as supply and demand fluctuate
- Other points of criticism relate, for example, to the lack of consideration of taxes
- These assumptions mean that the calculated prices may differ from the actual prices
Advantages and disadvantages of the Black Scholes model
The Black Scholes model offers some Advantages and leads to comparatively good estimates of prices. It can be used by anyone. The model is easy to use by entering the relevant parameters into the calculator in the formula. In addition, interest rates and volatility are taken into account, which can have a decisive influence.
Essential Disadvantages are the parameters that are not sufficiently taken into account. These include fluctuations in volatility, transaction costs and taxes. In addition, the model can only be used for European options.
Conclusion: Black Scholes explanation
In summary, the Black Scholes model is a model with certain assumptions and parameters that allows using a formula permitted, Calculate prices of derivatives and options.
It is important to take into account the basic assumptions of the model in order to Realistically assess the final result to be able to. Users should know, for example, that the Black Scholes model assumes constant interest rates.
The model has the advantage that precise calculations are possible that easy to implement are. Points of criticism refer to those parameters that are not taken into account in the model. These include, for example, taxes, changes in volatility and missing transaction costs.