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What Is the Black-Scholes Model?


We have seen the option pricing methods, Black Scholes Option Pricing Model is one among them. So, if you have not read our previous article on option pricing, you can check that here So, what is Black Scholes Option Pricing Model and why is the Black Scholes method Important.


Black Scholes is a method that is used in determining the fair price value of an option.

An option can be a call or put. Black Scholes method takes into consideration six variables to determine the fair price. These six factors are:

  1. Volatility,

  2. Time,

  3. Price of the underlying asset,

  4. Type of option,

  5. Strike price,

  6. Risk-free rate.

There are various methods for option pricing, among them Black- Scholes and Binomial models are widely used.


The Black Scholes method was developed in 1973 because of its effectiveness and accuracy, it is still considered the best way for calculating the theoretical value of an option contract. The black Scholes method was pioneered by Robert C Merton and Myron Scholes.


You might have a question Why Is Black Scholes Model Important or why should we do such an analysis? So, to answer this, let us explain Why Is Black Scholes Model is Important.


When an investor knows about the estimated fair value of the option, they can adjust their trading strategies and portfolios according to that price, therefore option pricing methods are very much useful for those involved in the financial market, mainly dealing in options trading.


Black Scholes Model Calculator: Many people have questions in their mind, is there any calculator in the market to calculate option pricing via Black Scholes Model? So, you will be glad to know that there are many calculators available online, some are free and some come with subscriptions, you may choose whichever you like based on your frequency of usage, and the accuracy you get using them.


In Black Scholes Model Calculator you have to provide the details, such as the strike price, volatility, and other variables and you will get the results in no time. The Black Scholes Model Calculator is a handy tool for investors and they can modify or change their trade or portfolio based on the theoretical price they get from these calculations.


So, how does an investor utilize this calculation? Investors buy those options that are calculated under the value and sell those that are priced higher than the calculated value.


Black Scholes Model Formula:


To calculate the theoretical value of the options you can use the below formula:


Call option Premium C = SN (d1) -Xe - rt N (d2)


Put option Premium P = Xe - rT N (-d2) - So N (-d1)


di = [ Ln (S/X) + (r+s2/2) X t ]


s Ot d2 = [Ln (S/X) + (r-s2/2) X t]


In the above formula,

C is the price of a call option

P is the price of a put option

S is the price of the underlying asset

X is the strike price

R is the rate of interest

T is the Expiration time

S is the volatility rate of an underlying asset

N stands for the normal distribution having a mean = 0 and a deviation = 1.


If you are not interested in calculating with the help of this formula, you may use Black-Scholes Option Pricing Calculator readily available online, or you may also contact your broker or advisor for the same.


Let us know some more facts about Black-Scholes Option Pricing Model.


  • This model can be helpful to know the price of the European call option which means only those options can be calculated that are to be exercised on the date of expiration.

  • There are a few assumptions in Black Scholes Option Pricing Model that there is no Transaction cost involved in buying the options, and the market volatility is constant. The returns are distributed normally (normal distribution).

  • It is a perfect fit with the delta hedging strategy of European options for non-dividend paying stocks.

  • Black Scholes model does not consider any interest rate, instead, it considers a risk-free rate.

  • Black Scholes model considers the Implied volatility as it can provide major benefits to the investors. Implied volatility can be said as the estimated variability of the underlying asset-option contact.

  • This model was first published in the " Journal of political economy" by Black Scholes in 1973

  • Robert C Merton also contributed to his work and published his work in an article named - "Theory of Rational Option pricing"

  • Mr, Black Scholes passed away in 1995.

  • In 1997, Both Mr. Black Scholes and Robert C Merton were given the Nobel Memorial prize for their work in the field of - “Economic Science”.

  • As Black was no longer alive so could not receive the prize, but he was acknowledged for the best work.


Conclusion

So, in this article, we have seen Black Scholes Option Pricing Model, how to calculate it manually with the help of the Black Scholes Model Formula, how does Black Scholes Model Calculator work, and also Black-Scholes Option Pricing Calculator. We hope the facts written about the Black Scholes model must have added some insights about the importance of this model and we hope we have done some value addition to your understanding regarding the what is Black Scholes model.



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