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Details:

Formula name:	Black Scholes Option Pricing
Author/Uploader:	Anthony Faragasso - ajf1111 [at] epix.net
Date/Time added:	2005-03-20 13:19:39
Origin:
Keywords:	Options, Black Scholes
Level:	advanced
Flags:	exploration

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Description:

Black Scholes Option Pricing returns the Fair Value of call and put options.

Formula:

//BLACK SHCOLES OPTION PRICING FORMULA
//coded by Anthony Faragasso
//1-01-03

// User Variables
 
StockPrice  = Param("stockPrice",81,1,200,1); //Stock Price 
Timedays    = Param("DaysToExpire",30,1,300,1); //Time to expiry ( days to
exp/365 )
StrikePrice = Param("StrikePrice",75,1,300,1); //strike Price of Option to
evaluate
InterestRate= Param("InterestRate",0.06,0.01,0.11,0.001); //prevailing interest
rate 
VKnown =Param("Volatility",0.30,0.10,0.50,0.001);//You can insert Known
volatility here , Implied Volatility. 

//////////////////////////////////////////////////////

time=timedays/365;// days to expire conversion formula


//Formula variables below

/*************************************************/
// Solves for ( X )

x = (ln(stockPrice/strikePrice) + (interestrate +
Vknown*Vknown/2)*time)/(Vknown*sqrt(time)); 
/*************************************************/

P =  0.2316419;   
bb1 = 0.31938153; 
bb2 = -0.3565638; 
bb3 = 1.78147794; 
bb4 = -1.821256;
bb5 = 1.33027443;

pi = 3.141592654; // PI

A2 = 1/sqrt(2*pi);
A3 = exp(-(x^2)/2);
y= a2*a3;
A4 = exp(-interestrate*time);
t1 = 1/(1+ P*x);
A5=(bb1*t1)+(bb2*t1^2) +( bb3*t1^3)+(bb4*t1^4)+(bb5*t1^5);
/************************************************************/
//Standard Normal Distribution Function of ( x )


N = 1- y *A5 ;

/************************************************************/
  // Solves for ( X1 )
X1=x-Vknown*sqrt(TIME);

y1=1/sqrt(2*pi);
N0=exp(-(x1^2)/2);
T2=1/(1+ P*X1);
A6=(bb1*t2)+(bb2*t2^2) +( bb3*t2^3)+(bb4*t2^4)+(bb5*t2^5);
A7=exp(-interestrate*time);
y2=y1*n0;

/************************************************************/
/* Standard Normal Distribution Function OF ( x1 )*/
/***********************************************************/
N2= 1-y2 * A6;

/************ CALL OPTION FAIR VALUE************/
Call = stockPrice  * N - strikePrice *  A4  * N2;

/************ PUT OPTION FAIR VALUE*************/

Put =  Call - stockprice  + strikeprice*A7;

 
Filter = 1;
SetOption("nodefaultcolumns",1);
AddColumn(stockPrice,"AssetP",2.2);
AddColumn(strikeprice,"StrikeP",1.2);
AddColumn(InterestRate*100,"InterestRate%",1.2);
AddColumn(VKnown*100,"Volatility%",1.2);
AddColumn(timedays,"DaysToExpire ",1);
AddColumn(Call,"Call FV",1.2);
AddColumn(put,"Put FV",1.2);

//Notes
/* AA window
1. Select current symbol ( could be any stock, output is not associated
with the current stock).
2. n last quotations
3. n = 1
4. Use the Parameters button to make user selections
5. Click explore */

Comments:

Hans

2005-03-27 10:01:30

Here follows code for use with stock relative to option as indicator:

//BLACK SCHOLES OPTION PRICING FORMULA
//coded by Anthony Faragasso
//1-01-03
/*modified by Hans 27/6/2005 for use as Indicator (use with amibroker 4.70)
** user have to copy/create into directory amibroker\formulas\include
following file named "DayToNumFunction.afl" with followin code:

function DayNum(dt)
{
yr= int(Dt/10000);
mo= int((dt-(yr*10000))/100);
dy= int(dt-(yr*10000)-(mo*100));
adj=(mo>1) +( mo>3) + (mo>5) + (mo>7) + (mo>8) + (mo>10) + (mo>12)- ((mo>2)*2);
return ( yr*365) +( (mo-1)*30) +dy +adj;
}

*/

#include <DayToNumFunction.afl>

// User Variables

//StockPrice = Param("stockPrice",81,0,200,0.001); //Stock Price
StockPrice = Close;
expdate = ParamDate( "Expiring date", "03/06/2005", 0 );
expdate=IIf(expdate>20000000,expdate-19000000,expdate);//correction (bug) of values
Timedays = daynum(expdate)-daynum(DateNum());
StrikePrice = Param("StrikePrice",0.9848,0,300,0.001); //strike Price of Option to evaluate
InterestRate= Param("InterestRate",0.025,0.01,0.11,0.001); //prevailing interest rate
VKnown =Param("Volatility",0.26,0.10,0.50,0.001);//You can insert Known volatility here , Implied Volatility.

//////////////////////////////////////////////////////

time=timedays/365;// days to expire conversion formula

//Formula variables below

/*************************************************/
// Solves for ( X )

x = (ln(stockPrice/strikePrice) + (interestrate + Vknown*Vknown/2)*time)/(Vknown*sqrt(time));
/*************************************************/

P = 0.2316419;
bb1 = 0.31938153;
bb2 = -0.3565638;
bb3 = 1.78147794;
bb4 = -1.821256;
bb5 = 1.33027443;

pi = 3.141592654; // PI

A2 = 1/sqrt(2*pi);
A3 = exp(-(x^2)/2);
y= a2*a3;
A4 = exp(-interestrate*time);
t1 = 1/(1+ P*x);
A5=(bb1*t1)+(bb2*t1^2) +( bb3*t1^3)+(bb4*t1^4)+(bb5*t1^5);
/************************************************************/
//Standard Normal Distribution Function of ( x )

N = 1- y *A5 ;

/************************************************************/
// Solves for ( X1 )
X1=x-Vknown*sqrt(TIME);

y1=1/sqrt(2*pi);
N0=exp(-(x1^2)/2);
T2=1/(1+ P*X1);
A6=(bb1*t2)+(bb2*t2^2) +( bb3*t2^3)+(bb4*t2^4)+(bb5*t2^5);
A7=exp(-interestrate*time);
y2=y1*n0;

/************************************************************/
/* Standard Normal Distribution Function OF ( x1 )*/
/***********************************************************/
N2= 1-y2 * A6;

/************ CALL OPTION FAIR VALUE************/
Call = stockPrice * N - strikePrice * A4 * N2;

/************ PUT OPTION FAIR VALUE*************/

Put = Call - stockprice + strikeprice*A7;
Plot(stockprice,Date()+" - Asset price",colorDarkBlue,styleLine|styleLeftAxisScale);
Plot(strikeprice,"Strike price = "+NumToStr(strikeprice,1.4),colorBlack,styleLine|styleLeftAxisScale);
Plot(InterestRate*100,"Interest rate",colorDarkGreen,styleOwnScale|styleNoLine|styleNoLabel);
Plot(VKnown*100,"Volatility%",colorDarkRed,styleOwnScale|styleNoLine|styleNoLabel);
Plot(timedays,"
DaysToExpire "+numtostr(expdate,10.0),colorDarkGrey,styleOwnScale|styleNoLine|styleNoLabel);
Plot(Call,"Call FV = "+NumToStr(Call,1.4),colorGreen,styleLine);
Plot(Put,"Put FV = "+NumToStr(put,1.4),colorRed,styleLine);

Filter = 1;
SetOption("nodefaultcolumns",1);
AddColumn(stockPrice,"AssetP",2.3);
AddColumn(strikeprice,"StrikeP",1.3);
AddColumn(InterestRate*100,"InterestRate%",1.2);
AddColumn(VKnown*100,"Volatility%",1.2);
AddColumn(timedays,"DaysToExpire ",1);
AddColumn(Call,"Call FV",1.4);
AddColumn(put,"Put FV",1.4);

//Notes
/* AA window
1. Select current symbol ( could be any stock, output is not associated
with the current stock).
2. n last quotations
3. n = 1
4. Use the Parameters button to make user selections
5. Click explore */