American Options – Pricing Methods and Spreadsheets

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This Options pricing spreadsheet Excel spreadsheet is intended to illustrate payoff and profit diagrams for option contracts. The user can specify up to four positions long or short in various instruments. The available instruments are stocks, riskfree bonds, puts, and calls. With puts and calls, the user specifies the options pricing spreadsheet price.

With bonds, the face value must be given by the user. This file is intended for use only by students enrolled in Finance courses at the Robinson College of Business at Georgia State University. However, if you would like to use this file in another setting, please contact the author of the spreadsheet Jason Greene for permission.

Download Instructions Click here to download the Microsoft Excel spreadsheet. If options pricing spreadsheet box appears asking for a username and password, click "Cancel" and the file should open. You should save the spreadsheet on your local disk in order to access it in the future. Spreadsheet Instructions The spreadsheet allows you to specify a strategy with up to four positions options pricing spreadsheet stocks, bonds, puts, or calls. The first worksheet in the Excel spreadsheet file is named "Payoffs" and demonstrates payoff diagrams only.

The second worksheet is named "Profits" and demonstrates both payoff and profit diagrams. Select the Graph type First select the graph type using the pop-up menu under the word "Graph" located options pricing spreadsheet to mid-left side of the spreadsheet. Choosing Payoff A will graph only the payoff diagram for position A in blue on the graph. Choosing Payoff All will graph all positions on the graph at the same time.

Choosing Payoff Combined will only graph the payoff diagram on the combined strategy of positions A through D. Similar graph types are available on the "Profits" worksheet. There are four possible positions A through D and the position color will correspond to the color of the curve on the graph. For example, the first instrument A is blue, so its payoff diagram on the graph will be blue. Options pricing spreadsheet "Profits" worksheet, the payoff diagram curves on the graph are thicker than the profit diagram curves, but are the same color.

Select each position To graph the payoff or profit diagrams, you must specify a position in at least one instrument. Choose the instrument you want from one of the four pop-up menus under the "Instrument" column.

For options, the Short position is when you "write" an options pricing spreadsheet. For bonds, the Short position is equivalent to borrowing money i. The diagram represented on the graph shows the payoff or profit at expiration or time of exercise for the options contracts. Each position is for one share of stock, an option on one share of stock, or one bond with the given face value.

So, if you want a position of two options pricing spreadsheet the same call options, for example, then you must specify identical call options for two separate positions e. To cancel a position, set the pop-up menu for the "Instrument" to blank the first pop-up menu choice. For example, setting all four positions A-D to a blank instrument gives you a blank graph. The option premium for a Call or Put position will appear options pricing spreadsheet the position is selected. The present value or price of the Bond will appear when the position is selected.

All options pricing spreadsheet are rounded to options pricing spreadsheet nearest 10 cents. Set the graph type to Payoff All to show both payoff diagrams from each position on the same graph. Or, set the graph type options pricing spreadsheet Payoff Combined to see only the payoff diagram of the strategy as a whole.

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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