Black-Scholes

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This page is a guide to creating your own option pricing Excel spreadsheet, in line with the Black-Scholes model extended for dividends by Merton. Here you can get a ready-made Black-Scholes Excel calculator with charts and additional features such as parameter calculations and simulations.

If you are not familiar with the Black-Scholes model, its parameters, and at least the logic of the formulas, you may first want to see this page. Below I will show you how to apply the Black-Scholes formulas in Excel and how to put them all together in a simple option pricing spreadsheet.

There are 4 steps:. First you need to design 6 cells for the 6 Black-Scholes parameters. When pricing a particular option, you will have to enter all the parameters in these cells in the correct format.

The parameters and formats are:. Underlying price is the price at which the underlying security is trading on the market at the moment you are doing the option pricing. Strike price , also called exercise price, is the price at which you will buy if call or sell if put the underlying security if you choose to exercise the option. If you need more explanation, see: Enter it also in dollars per share. Volatility is the most difficult parameter to estimate all the other parameters are more or less given.

It is your job to decide how high volatility you expect and what number to enter — neither the Black-Scholes model, nor this page will tell you how high volatility to expect with your particular option.

You can interpolate the yield curve to get the interest rate for your exact time to expiration. If you are pricing an option on securities other than stocks, you may enter the second country interest rate for FX options or convenience yield for commodities here. Alternatively, you may want to measure time in trading days rather than calendar days. Furthermore, you can also be more precise and measure time to expiration to hours or even minutes.

I will illustrate the calculations on the example below. You can of course start in row 1 or arrange your calculations in a column. When you have the cells with parameters ready, the next step is to calculate d1 and d2, because these terms then enter all the calculations of call and put option prices and Greeks. The formulas for d1 and d2 are:. All the operations in these formulas are relatively simple mathematics. The hardest on the d1 formula is making sure you put the brackets in the right places.

This is why you may want to calculate individual parts of the formula in separate cells, as I do in the example below:. First I calculate the natural logarithm of the ratio of underlying price and strike price in cell H Then I calculate the denominator of the d1 formula in cell J It is useful to calculate it separately like this, because this term will also enter the formula for d The two formulas are very similar.

There are 4 terms in each formula. I will again calculate them in separate cells first and then combine them in the final call and put formulas. Potentially unfamiliar parts of the formulas are the N d1 , N d2 , N -d2 , and N -d1 terms.

N x denotes the standard normal cumulative distribution function — for example, N d1 is the standard normal cumulative distribution function for the d1 that you have calculated in the previous step. DIST function, which has 4 parameters:. There is also the NORM. DIST, which provides greater flexibility. The exponents e-qt and e-rt terms are calculated using the EXP Excel function with -qt or -rt as parameter.

Here you can continue to the second part, which explains the formulas for delta, gamma, theta, vega, and rho in Excel:. Continue to Option Greeks Excel Formulas. Or you can see how all the Excel calculations work together in the Black-Scholes Calculator. If you don't agree with any part of this Agreement, please leave the website now.

All information is for educational purposes only and may be inaccurate, incomplete, outdated or plain wrong. Macroption is not liable for any damages resulting from using the content. No financial, investment or trading advice is given at any time. Home Calculators Tutorials About Contact. Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4.

The Big Picture If you are not familiar with the Black-Scholes model, its parameters, and at least the logic of the formulas, you may first want to see this page. There are 4 steps: Design cells where you will enter parameters. Calculate d1 and d2. Calculate call and put option prices. The parameters and formats are: Black-Scholes d1 and d2 Excel Formulas When you have the cells with parameters ready, the next step is to calculate d1 and d2, because these terms then enter all the calculations of call and put option prices and Greeks.

The formulas for d1 and d2 are: This is why you may want to calculate individual parts of the formula in separate cells, as I do in the example below: It is useful to calculate it separately like this, because this term will also enter the formula for d2: DIST function, which has 4 parameters: I calculate e-rt in cell Q