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## Black-Scholes Option Pricing Model formula

by The trader, 5507 days ago

This is a custom formula that calculates the put and call prices of European style options.

This Black-Scholes Option Pricing Model function accepts six parameters.
The first parameter is used to specify whether we want to calculate a put or a call, set 'p' for put and 'c' for call.
The others parameters are: Security price, strike price, years to maturity (if it is for example 6 month, then set '0.5'), risk-free rate and volatility.

The function calculates for each bar, the option price of a put or a call given the above parameters.
Set the Price parameters to 'close'.
For the volatility I usually use the following formula: Stddev(close, 30) * sqrt(1 / 12), that is the annualized historical volatility.
I used here the standard deviation for the past 30 days and then annualized the result.

If you set your formula to something like:
a = BlackScholes('c', close, 30, 0.25, 0.06, Stddev(close, 30) * sqrt(1 / 12)); // Option pricing formula
Plot(a, 'Pricing', colorBlack, chartLine, styleOwnScale);

The chart will display the option price of a call with a strike price of 30, 3 months to maturity, and 6% as risk-free rate.
Note: For each bar the number of days to maturity is constant and thus this is not the price of the call over time.

I use this function to create custom outputs to simulate option strategies.
For example, when I analyze a list of rules, instead of buying the stock, I use this formula to simulate a call or put buy or any other combination.

Note: this Black and Scholes formula should be modified in order to be able to calculate American style options.
Note also that this Option pricing model doesn't take dividends into account.

What is this?

 Type: Trading Indicator Object ID: 111 Country: All Market: Options Market Style: Technical Analysis

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