A calculation of option prices is possible by
using one of the following functions:
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The interactive option pricing quantlet
optstart
is simply
invoked by typing
optstart()in the XploRe command line. A selection box appears which starts the interactive option pricing procedure.
Simply select the method you want to use. If you wish to calculate the option price analytically, choose Black/Scholes & MC Millan; if you want XploRe to calculate it numerically, choose Binomial Tree. Let's choose Black/Scholes & MC Millan. In any case you will be asked whether you want to compute the price of an European (an option which can be executed only at a given date) or an American option (that can be executed anytime).
In this example we have chosen American. This is the kind of option that is usually traded e.g. in the USA or in Germany. The next decision is about the underlying asset (stock or exchange rate).
In our example we are regarding a stock as the underlying asset. In this setting you are questioned if you like to have dividends included in the stock and of what kind you want them to be. (If you choose Exchange Rate here, the next two menu items will be skipped.) Then you are asked whether you like to compute the price of an option or the implied volatility. Now we are ready to enter the parameters needed for the computation of the option prices. These are Price of the Underlying Asset, Exercise Price, Domestic Interest Rate per Year and Volatility per Year in percent as well as the Time to Expiration in years.
In case you have chosen a dividend payment, one more window will appear where you are asked to put the amount of the dividend.
Finally you can choose the kind of option you like to calculate. Let's say we wanted to know the price of a call option:
The price of our American call option on the given stock in the scenario (chosen through the corresponding parameters) with fixed dividend is now displayed in the XploRe output window. In case you have chosen a stock as underlying asset even the price of the European call option is displayed (in case you have not chosen a dividend, the price of a European call option equals that of an American call option):
[1,] [2,] ------------------------------------- [3,] The Price of Your European Call-Option [4,] on Given Stock with fixed Dividend is [5,] 27.3669 [6,] ------------------------------------- [7,] [1,] [2,] ------------------------------------- [3,] The Price of Your American Call-Option [4,] on Given Stock with fixed Dividend is [5,] 27.4641 [6,] ------------------------------------- [7,]
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The quantlet
influence
measures and visualizes the influence of
different factors on the prices of options. It is simply started by typing
influence()in the command line of XploRe. The option prices are calculated with the Black-Scholes formula. After starting the quantlet the following window appears:
You may enter the different parameters needed to simulate the diffusion process. Next select the influence variables -- you may select up to two variables. The following example demonstrates the use of just one variable:
In this example we would like to calculate the influence of the exercise price on the option price. You must set the lower and upper bound for your chosen variable.
After pushing the OK button you will be asked for what kind of option the influence is to be calculated.
If you choose for example a Put option you will obtain the following graph which shows the influence of the factor (exercise price) on the price of the option:
Using
influence
you can also select two variables
as the following example demonstrates:
After selecting the two variables you wish to compute, XploRe asks you to set the lower and upper bound for both variables.
If you choose e.g. Put you will obtain a three-dimensional graphic with the two selected influence factors (exercise price and time to expiration) and the price of the option. You may turn the graphic around by using the cursor buttons.
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The interactive function
greeks
calculates and displays
the different indices used for analyzing and trading with options.
You start it by
data=greeks()
The first step is to enter the asset's basic data:
Next, you have to select the variables you want to analyze (at most two), e.g.
Select the ranges for the values of the chosen variables:
Now you can choose the index you are interested in:
After telling the program the kind of option you want, the quantlet
greeks
will produce a graphical output window for your result:
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MD*TECH Method and Data Technologies |
http://www.mdtech.de mdtech@mdtech.de |