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This is the second part of the Black-Scholes Excel guide covering Excel calculations of option Greeks delta, gamma, theta, vega, and rho under the Black-Scholes model. I will continue in the example from the first part to demonstrate the exact Excel formulas. See the first part for details on parameters and Excel formulas for d1, d2, call price, and put price.
Here you can find detailed explanations of all the Black-Scholes formulas. Here you can see how everything works together in Excel in the Black-Scholes Calculator. Delta is different for call and put options.
The formulas for delta are relatively simple and so is the calculation in Excel. I calculate call delta in cell V44, continuing in the example from the first part , where I have already calculated the two individual terms in cells M44 and S The calculation of put delta is almost the same, using the same cells.
The formula for gamma is the same for calls and puts. It is slightly more complicated than the delta formulas above:. You will find this term in the calculation of theta and vega too. It is the standard normal probability density function for -d1. In Excel the formula looks like this:. Alternatively, you can use the NORM. In the example from the Black-Scholes Calculator I use the first formula.
The whole formula for gamma same for calls and puts is:. Theta has the longest formulas of all the five most common option Greeks. It is different for calls and puts, but the differences are again just a few minus signs here and there and you must be very careful.
Theta is very small for many options, which makes it often hard to detect a possible error in your calculations. Although it looks complicated, all the symbols and terms in the formulas should be already familiar from the calculations of option prices and delta and gamma above. One exception is the T at the beginning of the formulas. T is the number of days per year. Based on your selection, the interpretation of theta will then be either option price change in one calendar day or option price change in one trading day.
The whole formula for call theta in our example is in cell X It is long and uses several 10 other cells, but there is no high mathematics:. The last line of the formula in the screenshot above is the T. Cell C20 in the calculator contains a combo where users select calendar days or trading days. Cells D3 and D4 in the sheet Time Units contain the number of calendar and trading days per year. If you want to keep it simple, you can replace the whole last line of the formula with a fixed number, such as You can again find the explanation of all the individual cells in the first part or see all these Excel calculations directly in the calculator.
Rho is again different for calls and puts. There are two more minus signs in the put rho formula. In the calculator example I calculate call rho in cell Z It is simply a product of two parameters strike price and time to expiration and cells that I have already calculated in previous steps:. I calculate put rho in cell AF44, again as product of 4 other cells, divided by Make sure to put the minus sign to the beginning:.
You can also use Excel and the calculations above with some modifications and improvements to model behaviour of individual option Greeks and option prices in different market situations changes in the Black-Scholes model parameters. 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. Option Greeks Excel Formulas. Delta in Excel Delta is different for call and put options. It is slightly more complicated than the delta formulas above: Notice especially the second part of the formula: In Excel the formula looks like this: The whole formula for gamma same for calls and puts is: Call Option Theta The whole formula for call theta in our example is in cell X It is long and uses several 10 other cells, but there is no high mathematics: There is nothing new.
You can again see the familiar term at the end. In the calculator example I calculate vega in cell Y It is simply a product of two parameters strike price and time to expiration and cells that I have already calculated in previous steps: Make sure to put the minus sign to the beginning: