Re: [amibroker] Cumulative Normal Distr Function in AB

[Anthony Faragasso <ajf1111@xxxx>]

I do not know if you received the last email I sent to you, Here is an
updated black shcoles option pricing formula, the results match excel
exactly from about 15 points above stock price to any where below stock
price. Gives call Fair Value and Put Fair value.

As I said in Previous email, above 15 points excel and Ab do not match,
Ab seems to add a couple of points to the fair values, this is
something I am looking into.

Maybe, only Tomasz could answer that question. we shall see.

As for Normal Density Function:

N=1-1/sqrt(2*pi)*exp(-(x^2)/2)*(b1*t) +( b2*t^2) +(b3*t^3) +(b4*t^4) +
(b5*t^5)

where t = 1/1+p*x

b1 = 0.31938153
b2 = -0.3565638
b3 = 1.78147794
b4 = -1.821256
b5 = 1.33027443
P = 0.2316419

Hope this helps.
Anthony

myartast wrote:

> Hello,
>
> Please is anybody who can write or send me by e-mail the exact
> formula for Cumulative Normal Distr Function N(d) which I can use in
> AB?
> Thanks very much in advance.
>
> artast,
> artast@xxxx
>
>
> Yahoo! Groups Sponsor
ADVERTISEMENT


>
> Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.

//BLACK SHCOLES OPTION PRICING FORMULA
//Interpreted and coded by Anthony Faragasso

// Enter Variables

Vshort=0; // setting this variable, will use volatility of Market
// ( ex. setting to 20,is a 20 period historical volatility
StockPrice = 100; //Stock Price for testing( replace with Close ) 
Timedays = 182; //Time to expiry ( days to exp/365 )
StrikePrice = 120; //strike Price of Option to evaluate
InterestRate= 0.1; //prevailing interest rate 
V =0.2; //Setting Vshort to 0, you can insert Known volatility here. 
V = IIf(vshort > 0,StDev(log(C/Ref(C,-1)),Vshort)*sqrt(365)*100,V); 
time=timedays/365;// days to expire conversion for formula



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

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

P = 0.2316419; //0.33267; //koeficient 
bb1 = 0.31938153; //0.4361836; //koef
bb2 = -0.3565638; //-0.1201676; //koef
bb3 = 1.78147794; //0.937298; //koef
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-V*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;

AddColumn(stockPrice,"AssetP",2.2);
AddColumn(strikeprice,"StrikeP",1.2);
AddColumn(timedays,"DaysToExpire ",1);
AddColumn(Call,"Call FV",1.2);
AddColumn(put,"Put FV",1.2);

/************************************/
/* test columns */
AddColumn(x,"X",1.2);
AddColumn(A3,"a3",1.2);
AddColumn(n,"N",1.2);
AddColumn(t1,"t1",1.2);