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Here we can see a Japanese candlestick chart from the Nasdaq ETF. In the option trading jargon, the price of the stock is the underlying price.
Learning the 6 Parameters of Black Scholes Option Pricing Model
One of the first questions when learning how options trading works is what is the Black Scholes option pricing model used for and this is, calculating the option premium.
Obtaining this number can be quite a complicated matter and can lead to quite a few headaches.
We will explain why it is important to have a Black Scholes option pricing model calculator and what factors are involved in forming the premium. We will also learn how to make the Black Scholes calculation to use it in your own options trading.
Table of Contents
What is the Black Scholes model option pricing model used for?
The Black Scholes option pricing model is a mathematical model that provides the premium of the options for any given asset in any options market, for both calls and put options and for every strike price and expiration date of the option chain.
Take a look at this article if you still are not sure about how to read an option chain.
Why is it so important to have a Black Scholes model Excel at hand?
We should have a Black Scholes calculator Excel because we can easily read both premium and the greeks of every single trade.
If you need a free Black-Scholes model excel, you can always download our free template with our free option trading guide here:
How does the Black Scholes option pricing model Excel work?
The Black Scholes model Excel works simulating the exact theoretical model. It is a combination of six parameters we can obtain by looking at the option chains.
Of these six parameters, both options open interest and volume are not considered, so there might be some differences regarding the spread between the bid and the ask of every contract.
Let us take a look at the six parameters of the Black Scholes model.
The six main parameters necessary to provide to the Black Scholes option pricing model formula
1. The underlying price
The underlying price is the price value of the current asset the option refers to. It is the main parameter we are going to need in the Black Scholes calculator Excel.
2. The strike price of the option contract
The second parameter is the strike price of the call or put options we want to trade.
To add it to the Black Scholes Excel, the only thing we need to do is to pick which strike price of the option chain we want to trade. Depending on the strike we choose, we will have to more or less.
If you want to know more about how the relationships between the underlying and strike prices work, take a look at this article here.
We need to choose one strike price to our Black Scholes calculator Excel
3. Implied volatility
This is another of the most important parameters that we have to take into account when trading options, as it is the one that will cause us the most problems during our career as option traders.
The implied volatility that we have to pick to add to the Black Scholes model Excel is the one corresponding to the option chain whose strike price is the one we want.
This data usually appears in the option chains, since it is of great importance when trading. If you are not quite sure about what implied volatility is or how to deal with it, you can see how it works in this other article.
Do you need a Calculator that helps you create and analyze any option strategy in record time?
4. The time to expiration
The time factor is the fourth parameter we will need to determine the option premium in the Black Scholes calculator Excel. This data can be taken directly from the option chains. It is under the name of the expiration date.
To use it in the Black Scholes model Excel, we will only have to write it down in the corresponding cell.
5. Interest rates
Interest rates form the fifth parameter required to be able to use the Black-Scholes model formula.
Although this data is not very relevant when trading and it does not influence the model to any great extent, it is necessary if we want to create a proper Black Scholes model Excel.
The interest rates can be found by searching in the internet browser. Also, some brokers provide them directly within their option trading platforms.
If you want to know more about how interest rates affect the premium, you can check this article.
6. The Dividend
The last parameter is the dividend distributed by the investment fund or the company. Of course, if the underlying we are dealing with did not pay out any dividends, its value in the Black Scholes option pricing calculator would be zero.
To find out the total amount of dividends distributed, we can take a look at any financial newspaper, or we can consult the information provided by the broker.
As with interest rates, the dividend does not play a significant role in establishing the value of the option premium. However, as before, it is necessary to strictly replicate the Black-Scholes model calculator.
Have you just started with options or you still find some concepts confusing?
With the series of books Options Trading For Everyone you will learn everything you need to dominate the option market
What is the Black Scholes option pricing model formula?
Now that we have described the six parameters, let us take a look at the Black Scholes model formula needed to replicate the mathematical model to calculate the option price in case you want to build your own Black-Scholes option calculator.
Black Scholes option pricing model calculator formula d1 and d2
First of all, we are going to need to calculate two auxiliary parameters called d1 and d2. These are obtained as follows
In these case “ln” is the Neperian logarithm and “t” is the percentage of time to expiration, that was calculated as the number of days to expiration by 365 days.
Black Scholes option pricing model formula for option pricing
Now that we have both Black Scholes d1 and d2, the next step should be to calculate the option price for both call and put options. That is done by following the next formulas.
In these case, “N(d1)” and “N(d2)” are the Gaussian or Normal Distribution with mean equal to zero and standard deviation equal to one.
That would be the way to obtain the Black Scholes option pricing model calculator, but there is still some more information missing. To complete the Black Scholes calculator excel, we need to add the greeks.
If you want to learn how to add the greeks into the calculator, on this page you will find every option greek formula.
Our Free Black Scholes calculator Excel
As you can see, the Black Scholes option pricing model formula are somewhat complex to calculate, but the good thing is that once done, the model will provide us with any premium of any option, which will be extremely useful in our trading.
To make that task even easier, we have a Black Scholes option pricing model Excel for free
Last words about the Black Scholes option pricing model calculator
Having a replica of a Black-Scholes option pricing calculator is really important because there are many markets where those option premiums that are shown in the option chains do not correspond to the actual, real option premiums that should be.
The reason is because of the low volumes that can exist in an option chain, and there may be times when we might be paying too much without knowing it for sure.
That is why it is absolutely essential to have a proper Black Scholes option pricing model calculator at hand.
