다양한 언어로 표현한 블랙숄즈의 공식

아래는 “Black-Scholes” in Multiple Languages에서 일부를 옮겨왔습니다. 블로그 운영자인 Espen Gaarder Haug이 직접 개발한 소스뿐 아니라 인터넷에서 도움을 받은 자료들까지 망라하고 있습니다. 많이 사용하는 언어뿐 아니라 F#, Objective-C, Javascript, Perl, Python, O’calm까지 소개하고 있습니다. 원문을 보시면 더 많은 자료가 있습니다.

Black-Scholes in Visual Basic By Espen Gaarder Haug

'// The Black and Scholes (1973) Stock option formula
Public Function BlackScholes(CallPutFlag As String, S As Double, X _
As Double, T As Double, r As Double, v As Double) As Double

Dim d1 As Double, d2 As Double

d1 = (Log(S / X) + (r + v ^ 2 / 2) * T) / (v * Sqr(T))
d2 = d1 - v * Sqr(T)
If CallPutFlag = "c" Then
BlackScholes = S * CND(d1) - X * Exp(-r * T) * CND(d2)
ElseIf CallPutFlag = "p" Then
BlackScholes = X * Exp(-r * T) * CND(-d2) - S * CND(-d1)
End If
End Function

'// The cumulative normal distribution function
Public Function CND(X As Double) As Double

Dim L As Double, K As Double
Const a1 = 0.31938153: Const a2 = -0.356563782: Const a3 = 1.781477937:
Const a4 = -1.821255978: Const a5 = 1.330274429

L = Abs(X)
K = 1 / (1 + 0.2316419 * L)
CND = 1 - 1 / Sqr(2 * Application.Pi()) * Exp(-L ^ 2 / 2) * (a1 * K + a2 * K ^ 2 + a3 * K ^ 3 + a4 * K ^ 4 + a5 * K ^ 5)

If X < 0 Then
CND = 1 - CND
End If
End Function

'// The Black and Scholes (1973) Stock option formula

Public Function BlackScholes(CallPutFlag As String, S As Double, X _

As Double, T As Double, r As Double, v As Double) As Double

Dim d1 As Double, d2 As Double

d1 = (Log(S / X) + (r + v ^ 2 / 2) * T) / (v * Sqr(T))

d2 = d1 - v * Sqr(T)

If CallPutFlag = "c" Then

BlackScholes = S * CND(d1) - X * Exp(-r * T) * CND(d2)

ElseIf CallPutFlag = "p" Then

BlackScholes = X * Exp(-r * T) * CND(-d2) - S * CND(-d1)

End If

End Function

'// The cumulative normal distribution function

Public Function CND(X As Double) As Double

Dim L As Double, K As Double

Const a1 = 0.31938153: Const a2 = -0.356563782: Const a3 = 1.781477937:

Const a4 = -1.821255978: Const a5 = 1.330274429

L = Abs(X)

K = 1 / (1 + 0.2316419 * L)

CND = 1 - 1 / Sqr(2 * Application.Pi()) * Exp(-L ^ 2 / 2) * (a1 * K + a2 * K ^ 2 + a3 * K ^ 3 + a4 * K ^ 4 + a5 * K ^ 5)

If X < 0 Then

CND = 1 - CND

End If

End Function

Black-Scholes in C++ By Espen Gaarder Haug

#ifndef Pi 
#define Pi 3.141592653589793238462643 
#endif 

// The Black and Scholes (1973) Stock option formula
double BlackScholes(char CallPutFlag, double S, double X, double T, double r, double v)
{
double d1, d2;

d1=(log(S/X)+(r+v*v/2)*T)/(v*sqrt(T));
d2=d1-v*sqrt(T);

if(CallPutFlag == 'c')
return S *CND(d1)-X * exp(-r*T)*CND(d2);
else if(CallPutFlag == 'p')
return X * exp(-r * T) * CND(-d2) - S * CND(-d1);
}

// The cumulative normal distribution function 
double CND( double X )
{

double L, K, w ;

double const a1 = 0.31938153, a2 = -0.356563782, a3 = 1.781477937;
double const a4 = -1.821255978, a5 = 1.330274429;

L = fabs(X);
K = 1.0 / (1.0 + 0.2316419 * L);
w = 1.0 - 1.0 / sqrt(2 * Pi) * exp(-L *L / 2) * (a1 * K + a2 * K *K + a3 * pow(K,3) + a4 * pow(K,4) + a5 * pow(K,5));

if (X < 0 ){
w= 1.0 - w;
}
return w;
}

#ifndef Pi

#define Pi 3.141592653589793238462643

#endif

// The Black and Scholes (1973) Stock option formula

double BlackScholes(char CallPutFlag, double S, double X, double T, double r, double v)

{

double d1, d2;

d1=(log(S/X)+(r+v*v/2)*T)/(v*sqrt(T));

d2=d1-v*sqrt(T);

if(CallPutFlag == 'c')

return S *CND(d1)-X * exp(-r*T)*CND(d2);

else if(CallPutFlag == 'p')

return X * exp(-r * T) * CND(-d2) - S * CND(-d1);

}

// The cumulative normal distribution function

double CND( double X )

{

double L, K, w ;

double const a1 = 0.31938153, a2 = -0.356563782, a3 = 1.781477937;

double const a4 = -1.821255978, a5 = 1.330274429;

L = fabs(X);

K = 1.0 / (1.0 + 0.2316419 * L);

w = 1.0 - 1.0 / sqrt(2 * Pi) * exp(-L *L / 2) * (a1 * K + a2 * K *K + a3 * pow(K,3) + a4 * pow(K,4) + a5 * pow(K,5));

if (X < 0 ){

w= 1.0 - w;

}

return w;

}

Black-Scholes in JAVA By Espen Gaarder Haug

// The Black and Scholes (1973) Stock option formula

public double BlackScholes(char CallPutFlag, double S, double X, double T, double r, double v)
{
double d1, d2;

d1=(Math.log(S/X)+(r+v*v/2)*T)/(v*Math.sqrt(T));
d2=d1-v*Math.sqrt(T);

if (CallPutFlag=='c')
{
return S*CND(d1)-X*Math.exp(-r*T)*CND(d2);
}
else
{
return X*Math.exp(-r*T)*CND(-d2)-S*CND(-d1);
}
}

// The cumulative normal distribution function 
public double CND(double X)
{
double L, K, w ;
double a1 = 0.31938153, a2 = -0.356563782, a3 = 1.781477937, a4 = -1.821255978, a5 = 1.330274429;

L = Math.abs(X);
K = 1.0 / (1.0 + 0.2316419 * L);
w = 1.0 - 1.0 / Math.sqrt(2.0 * Math.PI) * Math.exp(-L *L / 2) * (a1 * K + a2 * K *K + a3 
* Math.pow(K,3) + a4 * Math.pow(K,4) + a5 * Math.pow(K,5));

if (X < 0.0) 
{
w= 1.0 - w;
}
return w;
}

// The Black and Scholes (1973) Stock option formula

public double BlackScholes(char CallPutFlag, double S, double X, double T, double r, double v)

{

double d1, d2;

d1=(Math.log(S/X)+(r+v*v/2)*T)/(v*Math.sqrt(T));

d2=d1-v*Math.sqrt(T);

if (CallPutFlag=='c')

{

return S*CND(d1)-X*Math.exp(-r*T)*CND(d2);

}

else

{

return X*Math.exp(-r*T)*CND(-d2)-S*CND(-d1);

}

// The cumulative normal distribution function

public double CND(double X)

{

double L, K, w ;

double a1 = 0.31938153, a2 = -0.356563782, a3 = 1.781477937, a4 = -1.821255978, a5 = 1.330274429;

L = Math.abs(X);

K = 1.0 / (1.0 + 0.2316419 * L);

w = 1.0 - 1.0 / Math.sqrt(2.0 * Math.PI) * Math.exp(-L *L / 2) * (a1 * K + a2 * K *K + a3

* Math.pow(K,3) + a4 * Math.pow(K,4) + a5 * Math.pow(K,5));

if (X < 0.0)

{

w= 1.0 - w;

}

return w;

}

Black-Scholes in Java Script By Espen Gaarder Haug

/* The Black and Scholes (1973) Stock option formula */

function BlackScholes(PutCallFlag, S, X, T, r, v) {

var d1, d2;
d1 = (Math.log(S / X) + (r + v * v / 2.0) * T) / (v * Math.sqrt(T));
d2 = d1 - v * Math.sqrt(T);

if (PutCallFlag== "c")
return S * CND(d1)-X * Math.exp(-r * T) * CND(d2);
else
return X * Math.exp(-r * T) * CND(-d2) - S * CND(-d1);

}

/* The cummulative Normal distribution function: */

function CND(x){

var a1, a2, a3, a4 ,a5, k ;

a1 = 0.31938153, a2 =-0.356563782, a3 = 1.781477937, a4= -1.821255978 , a5= 1.330274429;

if(x<0.0)
return 1-CND(-x);
else
k = 1.0 / (1.0 + 0.2316419 * x);
return 1.0 - Math.exp(-x * x / 2.0)/ Math.sqrt(2*Math.PI) * k
* (a1 + k * (-0.356563782 + k * (1.781477937 + k * (-1.821255978 + k * 1.330274429)))) ;

}

/* The Black and Scholes (1973) Stock option formula */

function BlackScholes(PutCallFlag, S, X, T, r, v) {

var d1, d2;

d1 = (Math.log(S / X) + (r + v * v / 2.0) * T) / (v * Math.sqrt(T));

d2 = d1 - v * Math.sqrt(T);

if (PutCallFlag== "c")

return S * CND(d1)-X * Math.exp(-r * T) * CND(d2);

else

return X * Math.exp(-r * T) * CND(-d2) - S * CND(-d1);

}

/* The cummulative Normal distribution function: */

function CND(x){

var a1, a2, a3, a4 ,a5, k ;

a1 = 0.31938153, a2 =-0.356563782, a3 = 1.781477937, a4= -1.821255978 , a5= 1.330274429;

if(x<0.0)

return 1-CND(-x);

else

k = 1.0 / (1.0 + 0.2316419 * x);

return 1.0 - Math.exp(-x * x / 2.0)/ Math.sqrt(2*Math.PI) * k

* (a1 + k * (-0.356563782 + k * (1.781477937 + k * (-1.821255978 + k * 1.330274429)))) ;

}

Black-Scholes in Perl By Jerome V. Braun

=head2 BlackScholes

Routine to implement the Black and Scholes (1973) option pricing formula.

# usage
$price = GBlackScholes($call_put_flag, $S, $X, $T, $r, $b, $v);

Here C<$call_put_flag> is either 'c' or 'p' for a call or put respectively,

=cut

sub BlackScholes {
my ($call_put_flag, $S, $X, $T, $r, $v) = @_;

# calculate some auxiliary values
my $d1 = ( log($S/$X) + ($r+$v**2/2)*$T ) / ( $v * $T**0.5 );
my $d2 = $d1 - $v * $T**0.5;

if ($call_put_flag eq 'c') {
return $S * &CND($d1) - $X * exp( -$r * $T ) * &CND($d2);
}
else { # ($call_put_flag eq 'p')
return $X * exp( -$r * $T ) * &CND(-$d2) - $S * &CND(-$d1);
}

}

=head2 CND

Approximate the cumulative normal distribution. That is, the value
of the integral of the standard normal density from minus infinity
to C<$x>.

# usage
$p = &CND($x);

=cut

sub CND {
my $x = shift;

# the percentile under consideration

my $Pi = 3.141592653589793238;

# Taylor series coefficients
my ($a1, $a2, $a3, $a4, $a5) = (0.319381530, -0.356563782, 1.781477937, -1.821255978, 1.330274429);

# use symmetry to perform the calculation to the right of 0
my $L = abs($x);

my $k = 1/( 1 + 0.2316419*$L);

my $CND = 1 - 1/(2*$Pi)**0.5 * exp(-$L**2/2)
* ($a1*$k + $a2*$k**2 + $a3*$k**3 + $a4*$k**4 + $a5*$k**5);

# then return the appropriate value
return ($x >= 0) ? $CND : 1-$CND;

}

=head2 BlackScholes

Routine to implement the Black and Scholes (1973) option pricing formula.

# usage

$price = GBlackScholes($call_put_flag, $S, $X, $T, $r, $b, $v);

Here C<$call_put_flag> is either 'c' or 'p' for a call or put respectively,

=cut

sub BlackScholes {

my ($call_put_flag, $S, $X, $T, $r, $v) = @_;

# calculate some auxiliary values

my $d1 = ( log($S/$X) + ($r+$v**2/2)*$T ) / ( $v * $T**0.5 );

my $d2 = $d1 - $v * $T**0.5;

if ($call_put_flag eq 'c') {

return $S * &CND($d1) - $X * exp( -$r * $T ) * &CND($d2);

}

else { # ($call_put_flag eq 'p')

return $X * exp( -$r * $T ) * &CND(-$d2) - $S * &CND(-$d1);

}

=head2 CND

Approximate the cumulative normal distribution. That is, the value

of the integral of the standard normal density from minus infinity

to C<$x>.

# usage

$p = &CND($x);

=cut

sub CND {

my $x = shift;

# the percentile under consideration

my $Pi = 3.141592653589793238;

# Taylor series coefficients

my ($a1, $a2, $a3, $a4, $a5) = (0.319381530, -0.356563782, 1.781477937, -1.821255978, 1.330274429);

# use symmetry to perform the calculation to the right of 0

my $L = abs($x);

my $k = 1/( 1 + 0.2316419*$L);

my $CND = 1 - 1/(2*$Pi)**0.5 * exp(-$L**2/2)

* ($a1*$k + $a2*$k**2 + $a3*$k**3 + $a4*$k**4 + $a5*$k**5);

# then return the appropriate value

return ($x >= 0) ? $CND : 1-$CND;

}

Black-Scholes in Delphi/Pascal By Desmond Nolan, Advanced Business Continuity Systems, Inc.

function BlackScholes(CallPutFlag : string; S, X, T, r, v : Double) :

Double;

var

  d1, d2 : Double;

begin

  Result := 0;

  d1 := (LN(S / X) + (r + Power(v, 2) / 2) * T) / (v * SqRt(T));

  d2 := d1 - v * SqRt(T);

  if CallPutFlag = 'c' then

    Result := S * CND(d1) - X * Exp(-r * T) * CND(d2)

  else

    if CallPutFlag = 'p' then

      Result := X * Exp(-r * T) * CND(-d2) - S * CND(-d1);

end;
{The cumulative normal distribution function}

function CND(X : Double) : Double;

var

  L, K : Double;

const

  a1 = 0.31938153;   a2 = -0.356563782;  a3 = 1.781477937;

  a4 = -1.821255978; a5 = 1.330274429;

begin

  L := Abs(X);

  K := 1 / (1 + 0.2316419 * L);

  Result := 1 - 1 / SqRt(2 * Pi) * Exp(-Power(L, 2) / 2)

            * (a1 * K + a2 * Power(K, 2) + a3 * Power(K, 3)

            + a4 * Power(K, 4) + a5 * Power(K, 5));

  if X < 0 then

    Result := (1 - Result)

end;

function BlackScholes(CallPutFlag : string; S, X, T, r, v : Double) :

Double;

var

d1, d2 : Double;

begin

Result := 0;

d1 := (LN(S / X) + (r + Power(v, 2) / 2) * T) / (v * SqRt(T));

d2 := d1 - v * SqRt(T);

if CallPutFlag = 'c' then

Result := S * CND(d1) - X * Exp(-r * T) * CND(d2)

else

if CallPutFlag = 'p' then

Result := X * Exp(-r * T) * CND(-d2) - S * CND(-d1);

end;

{The cumulative normal distribution function}

function CND(X : Double) : Double;

var

L, K : Double;

const

a1 = 0.31938153; a2 = -0.356563782; a3 = 1.781477937;

a4 = -1.821255978; a5 = 1.330274429;

begin

L := Abs(X);

K := 1 / (1 + 0.2316419 * L);

Result := 1 - 1 / SqRt(2 * Pi) * Exp(-Power(L, 2) / 2)

* (a1 * K + a2 * Power(K, 2) + a3 * Power(K, 3)

+ a4 * Power(K, 4) + a5 * Power(K, 5));

if X < 0 then

Result := (1 - Result)

end;

Black-Scholes in Python By Andy Smith

from math import *
# Cumulative normal distribution

def CND(X):

    (a1,a2,a3,a4,a5) = (0.31938153, -0.356563782, 1.781477937, 

     -1.821255978, 1.330274429)
    L = abs(X)

    K = 1.0 / (1.0 + 0.2316419 * L)

    w = 1.0 - 1.0 / sqrt(2*pi)*exp(-L*L/2.) * (a1*K + a2*K*K + a3*pow(K,3) +

    a4*pow(K,4) + a5*pow(K,5))
    if X<0:

        w = 1.0-w

    return w
# Black Sholes Function

def BlackSholes(CallPutFlag,S,X,T,r,v):

    d1 = (log(S/X)+(r+v*v/2.)*T)/(v*sqrt(T))

    d2 = d1-v*sqrt(T)
    if CallPutFlag=='c':

        return S*CND(d1)-X*exp(-r*T)*CND(d2)

    else:

        return X*exp(-r*T)*CND(-d2)-S*CND(-d1)

from math import *

# Cumulative normal distribution

def CND(X):

(a1,a2,a3,a4,a5) = (0.31938153, -0.356563782, 1.781477937,

-1.821255978, 1.330274429)

L = abs(X)

K = 1.0 / (1.0 + 0.2316419 * L)

w = 1.0 - 1.0 / sqrt(2*pi)*exp(-L*L/2.) * (a1*K + a2*K*K + a3*pow(K,3) +

a4*pow(K,4) + a5*pow(K,5))

if X<0:

w = 1.0-w

return w

# Black Sholes Function

def BlackSholes(CallPutFlag,S,X,T,r,v):

d1 = (log(S/X)+(r+v*v/2.)*T)/(v*sqrt(T))

d2 = d1-v*sqrt(T)

if CallPutFlag=='c':

return S*CND(d1)-X*exp(-r*T)*CND(d2)

else:

return X*exp(-r*T)*CND(-d2)-S*CND(-d1)

Black-Scholes in Fortran By Lance McKinzie and John Matovu

! The Black and Scholes (1973) Stock option formula

Real*8 Function BlackScholes(CallPutFlag, S, X, T, r, v)

      character*1 CallPutFlag

      real*8 S,X,T,r,v

	real*8 d1, d2

	d1 = (Log(S / X) + (r + v**2. / 2.) * T) / (v * Sqrt(T))

	d2 = d1 - v * Sqrt(T)

	If (CallPutFlag.eq.'c') Then

		BlackScholes = S * CND(d1) - X * Exp(-r * T) * CND(d2)

	ElseIf( CallPutFlag.eq.'p') Then

		BlackScholes = X * Exp(-r * T) * CND(-d2) - S * CND(-d1)

	End If

	Return

End
! The cumulative normal distribution function

	Real*8 Function CND(X)

	PARAMETER (DPI=3.141592653589793238D0)

	real*8 X

	real*8 L, K

	real*8 a1,a2,a3,a4,a5

	a1 = 0.31938153

	a2 = -0.356563782

	a3 = 1.781477937

	a4 = -1.821255978

	a5 = 1.330274429

	L = Abs(X)

	K = 1. / (1. + 0.2316419 * L)

	CND = 1. -1./Sqrt(2. * DPI) * Exp(-L**2. / 2.) * 

	1	(a1 * K + a2 * K**2. + a3 * K**3. + a4 * K**4. + a5 * K**5.)

	If (X.lt.0.) Then

		CND = 1. - CND

	End If

	Return

End

! The Black and Scholes (1973) Stock option formula

Real*8 Function BlackScholes(CallPutFlag, S, X, T, r, v)

character*1 CallPutFlag

real*8 S,X,T,r,v

real*8 d1, d2

d1 = (Log(S / X) + (r + v**2. / 2.) * T) / (v * Sqrt(T))

d2 = d1 - v * Sqrt(T)

If (CallPutFlag.eq.'c') Then

BlackScholes = S * CND(d1) - X * Exp(-r * T) * CND(d2)

ElseIf( CallPutFlag.eq.'p') Then

BlackScholes = X * Exp(-r * T) * CND(-d2) - S * CND(-d1)

End If

Return

End

! The cumulative normal distribution function

Real*8 Function CND(X)

PARAMETER (DPI=3.141592653589793238D0)

real*8 X

real*8 L, K

real*8 a1,a2,a3,a4,a5

a1 = 0.31938153

a2 = -0.356563782

a3 = 1.781477937

a4 = -1.821255978

a5 = 1.330274429

L = Abs(X)

K = 1. / (1. + 0.2316419 * L)

CND = 1. -1./Sqrt(2. * DPI) * Exp(-L**2. / 2.) *

1 (a1 * K + a2 * K**2. + a3 * K**3. + a4 * K**4. + a5 * K**5.)

If (X.lt.0.) Then

CND = 1. - CND

End If

Return

End

Black-Scholes in php By Franiatte Xavier

function CND ($x) {

$Pi = 3.141592653589793238;

$a1 = 0.319381530;

$a2 = -0.356563782;

$a3 = 1.781477937;

$a4 = -1.821255978;

$a5 = 1.330274429;

$L = abs($x);

$k = 1 / ( 1 + 0.2316419 * $L);

$p = 1 - 1 /  pow(2 * $Pi, 0.5) * exp( -pow($L, 2) / 2 ) * ($a1 * $k + $a2 * pow($k, 2)

     + $a3 * pow($k, 3) + $a4 * pow($k, 4) + $a5 * pow($k, 5) );

if ($x >= 0) { 

return $p;

} else {

return 1-$p;

}

}
function BlackScholes ($call_put_flag, $S, $X, $T, $r, $v) 

 {

$d1 = ( log($S / $X) + ($r + pow($v, 2) / 2) * $T ) / ( $v * pow($T, 0.5) );

$d2 = $d1 - $v * pow($T, 0.5);

if ($call_put_flag == 'c') {

return $S * CND($d1) - $X * exp( -$r * $T ) * CND($d2);

} else { 

return $X * exp( -$r * $T ) * CND(-$d2) - $S * CND(-$d1);

}

function CND ($x) {

$Pi = 3.141592653589793238;

$a1 = 0.319381530;

$a2 = -0.356563782;

$a3 = 1.781477937;

$a4 = -1.821255978;

$a5 = 1.330274429;

$L = abs($x);

$k = 1 / ( 1 + 0.2316419 * $L);

$p = 1 - 1 / pow(2 * $Pi, 0.5) * exp( -pow($L, 2) / 2 ) * ($a1 * $k + $a2 * pow($k, 2)

+ $a3 * pow($k, 3) + $a4 * pow($k, 4) + $a5 * pow($k, 5) );

if ($x >= 0) {

return $p;

} else {

return 1-$p;

}

function BlackScholes ($call_put_flag, $S, $X, $T, $r, $v)

{

$d1 = ( log($S / $X) + ($r + pow($v, 2) / 2) * $T ) / ( $v * pow($T, 0.5) );

$d2 = $d1 - $v * pow($T, 0.5);

if ($call_put_flag == 'c') {

return $S * CND($d1) - $X * exp( -$r * $T ) * CND($d2);

} else {

return $X * exp( -$r * $T ) * CND(-$d2) - $S * CND(-$d1);

}

Black-Scholes in O’Caml By Andrey A. Kolessa, OILspace inc. Moscow Office

(* 
   Objective Caml is a fast modern type-inferring functional programming 
language 
   descended from the ML (Meta Language) family.
   O'Caml is as fast as C/C++ 
   http://www.ocaml.org/
*)

let pow x n = exp ((float_of_int n) *. log(x) ) ;;
(* The cumulative normal distribution function *)
let cnd x =
   let a1 = 0.31938153 and a2= -0.356563782 and a3=1.781477937 and a4= 
-1.821255978 and a5=1.330274429 in
   let pi = 4.0 *. atan 1.0 in
   let l  = abs_float(x) in
   let k  = 1.0 /. (1.0 +. 0.2316419 *. l) in
   let w  = ref (1.0-.1.0/.sqrt(2.0*.pi)*.exp(-.l*.l/.2.0)*.(a1*.k+.a2*
.k*.k+.a3*.
            (pow k 3)+.a4*.(pow k 4)+.a5*.(pow k 5))) in
   if (x < 0.0) then  w := 1.0 -. !w ;
!w
(* The Black and Scholes (1973) Stock option formula *)
let black_scholes call_put_flag s x t r v = 
   let d1=(log(s /. x) +. (r+.v*.v/.2.0)*.t)/.(v*.sqrt(t)) in
   let d2=d1-.v*.sqrt(t) in
   let res = ref 0.0 in
   if (call_put_flag == 'c') then
      res := s*.cnd(d1)-.x*.exp(-.r*.t)*.cnd(d2)
   else
      res := x*.exp(-.r*.t)*.cnd(-.d2)-.s*.cnd(-.d1);
!res

Objective Caml is a fast modern type-inferring functional programming

language

descended from the ML (Meta Language) family.

O'Caml is as fast as C/C++

http://www.ocaml.org/

let pow x n = exp ((float_of_int n) *. log(x) ) ;;

(* The cumulative normal distribution function *)

let cnd x =

let a1 = 0.31938153 and a2= -0.356563782 and a3=1.781477937 and a4=

-1.821255978 and a5=1.330274429 in

let pi = 4.0 *. atan 1.0 in

let l = abs_float(x) in

let k = 1.0 /. (1.0 +. 0.2316419 *. l) in

let w = ref (1.0-.1.0/.sqrt(2.0*.pi)*.exp(-.l*.l/.2.0)*.(a1*.k+.a2*

.k*.k+.a3*.

(pow k 3)+.a4*.(pow k 4)+.a5*.(pow k 5))) in

if (x < 0.0) then w := 1.0 -. !w ;

(* The Black and Scholes (1973) Stock option formula *)

let black_scholes call_put_flag s x t r v =

let d1=(log(s /. x) +. (r+.v*.v/.2.0)*.t)/.(v*.sqrt(t)) in

let d2=d1-.v*.sqrt(t) in

let res = ref 0.0 in

if (call_put_flag == 'c') then

res := s*.cnd(d1)-.x*.exp(-.r*.t)*.cnd(d2)

else

res := x*.exp(-.r*.t)*.cnd(-.d2)-.s*.cnd(-.d1);

!res

Black-Scholes in Transact SQL By Nazy Norouzy

--Black Scholes Function:
create Function BlackScholes(@CallPutFlag varchar(100), @S float, @X float, 
@T float, @r float, @v float) 
returns float
as
begin
declare @d1 float
declare @d2 float
declare @BS float
set @d1 = (Log(@S / @X) + (@r + power(@v,2) / 2) * @T) / (@v * Sqrt(@T))
set @d2 = @d1 - @v * Sqrt(@T)
If @CallPutFlag = 'c'
begin
	set @BS = @S * dbo.CND(@d1) - @X * Exp(-@r * @T) * dbo.CND(@d2)
end 
else
    If @CallPutFlag = 'p'
    begin
	set @BS = @X * Exp(-@r * @T) * dbo.CND(-@d2) - @S * dbo.CND(-@d1)
    End 
return @BS
End
------------------------------------------
-- The cumulative normal distribution function:
create Function CND(@X float) 
returns float
as 
begin
declare @L float
declare @K float
declare @a1 float
declare @a2 float
declare @a3 float
declare @a4 float
declare @a5 float
set @a1 = 0.31938153
set @a2 = -0.356563782
set @a3 = 1.781477937
set @a4 = -1.821255978
set @a5 = 1.330274429
set @L = Abs(@X)
set @K = 1 / (1 + 0.2316419 * @L)
declare @CND1 float
set @CND1 = 1 - 1 / Sqrt(2 * Pi()) * Exp(-power(@L,2) / 2) * (@a1 * @K + 
@a2 * power(@K,2) + @a3 * power(@K,3) + @a4 * power(@K,4) + @a5 * 
power(@K,5))
If @X &lt; 0 
begin
	set @CND1 = 1 - @CND1
End
return @CND1
End

--Black Scholes Function:

create Function BlackScholes(@CallPutFlag varchar(100), @S float, @X float,

@T float, @r float, @v float)

returns float

begin

declare @d1 float

declare @d2 float

declare @BS float

set @d1 = (Log(@S / @X) + (@r + power(@v,2) / 2) * @T) / (@v * Sqrt(@T))

set @d2 = @d1 - @v * Sqrt(@T)

If @CallPutFlag = 'c'

begin

set @BS = @S * dbo.CND(@d1) - @X * Exp(-@r * @T) * dbo.CND(@d2)

end

else

If @CallPutFlag = 'p'

begin

set @BS = @X * Exp(-@r * @T) * dbo.CND(-@d2) - @S * dbo.CND(-@d1)

End

return @BS

End

------------------------------------------

-- The cumulative normal distribution function:

create Function CND(@X float)

returns float

begin

declare @L float

declare @K float

declare @a1 float

declare @a2 float

declare @a3 float

declare @a4 float

declare @a5 float

set @a1 = 0.31938153

set @a2 = -0.356563782

set @a3 = 1.781477937

set @a4 = -1.821255978

set @a5 = 1.330274429

set @L = Abs(@X)

set @K = 1 / (1 + 0.2316419 * @L)

declare @CND1 float

set @CND1 = 1 - 1 / Sqrt(2 * Pi()) * Exp(-power(@L,2) / 2) * (@a1 * @K +

@a2 * power(@K,2) + @a3 * power(@K,3) + @a4 * power(@K,4) + @a5 *

power(@K,5))

If @X < 0

begin

set @CND1 = 1 - @CND1

End

return @CND1

End

Black-Scholes in C# By Robert Derby

namespace BlackScholes
{
	/// <summary>
	/// Summary description for BlackSholes.
	/// </summary>
	public class BlackSholes
	{
		public BlackSholes()
		{
			//
			// TODO: Add constructor logic here
			//
		}
		/* The Black and Scholes (1973) Stock option formula
		 * C# Implementation
		 * uses the C# Math.PI field rather than a constant as in the C++ implementaion
		 * the value of Pi is 3.14159265358979323846
		*/
		public double BlackScholes(string CallPutFlag, double S, double X, 
			double T, double r, double v)
		{
			double d1 = 0.0;
			double d2 = 0.0;
			double dBlackScholes = 0.0;

			d1 = (Math.Log(S / X) + (r + v * v / 2.0) * T) / (v * Math.Sqrt(T));
			d2 = d1 - v * Math.Sqrt(T);
			if (CallPutFlag == "c")
			{				
				dBlackScholes = S * CND(d1) - X * Math.Exp(-r * T) * CND(d2);
			}
			else if (CallPutFlag == "p") 
			{
				dBlackScholes = X * Math.Exp(-r * T) * CND(-d2) - S * CND(-d1);				
			}
			return dBlackScholes;
		}
		public double CND(double X)
		{
			double L = 0.0;
			double K = 0.0;
			double dCND = 0.0;
			const double a1 = 0.31938153; 
			const double a2 = -0.356563782; 
			const double a3 = 1.781477937;
			const double a4 = -1.821255978;
			const double a5 = 1.330274429;
			L = Math.Abs(X);
			K = 1.0 / (1.0 + 0.2316419 * L);
			dCND = 1.0 - 1.0 / Math.Sqrt(2 * Convert.ToDouble(Math.PI.ToString())) * 
				Math.Exp(-L * L / 2.0) * (a1 * K + a2 * K  * K + a3 * Math.Pow(K, 3.0) + 
				a4 * Math.Pow(K, 4.0) + a5 * Math.Pow(K, 5.0));

			if (X < 0) 
			{
				return 1.0 - dCND;
			}
			else
			{
				return dCND;
			}
		}
	}
}

namespace BlackScholes

{

/// <summary>

/// Summary description for BlackSholes.

/// </summary>

public class BlackSholes

{

public BlackSholes()

{

// TODO: Add constructor logic here

}

/* The Black and Scholes (1973) Stock option formula

* C# Implementation

* uses the C# Math.PI field rather than a constant as in the C++ implementaion

* the value of Pi is 3.14159265358979323846

public double BlackScholes(string CallPutFlag, double S, double X,

double T, double r, double v)

{

double d1 = 0.0;

double d2 = 0.0;

double dBlackScholes = 0.0;

d1 = (Math.Log(S / X) + (r + v * v / 2.0) * T) / (v * Math.Sqrt(T));

d2 = d1 - v * Math.Sqrt(T);

if (CallPutFlag == "c")

{

dBlackScholes = S * CND(d1) - X * Math.Exp(-r * T) * CND(d2);

}

else if (CallPutFlag == "p")

{

dBlackScholes = X * Math.Exp(-r * T) * CND(-d2) - S * CND(-d1);

}

return dBlackScholes;

}

public double CND(double X)

{

double L = 0.0;

double K = 0.0;

double dCND = 0.0;

const double a1 = 0.31938153;

const double a2 = -0.356563782;

const double a3 = 1.781477937;

const double a4 = -1.821255978;

const double a5 = 1.330274429;

L = Math.Abs(X);

K = 1.0 / (1.0 + 0.2316419 * L);

dCND = 1.0 - 1.0 / Math.Sqrt(2 * Convert.ToDouble(Math.PI.ToString())) *

Math.Exp(-L * L / 2.0) * (a1 * K + a2 * K * K + a3 * Math.Pow(K, 3.0) +

a4 * Math.Pow(K, 4.0) + a5 * Math.Pow(K, 5.0));

if (X < 0)

{

return 1.0 - dCND;

}

else

{

return dCND;

}

Black-Scholes in PL/SQL By Fernardo Casteras, Bunos Aires, Argentina

CREATE OR REPLACE FUNCTION BLACKSCHOLES ( CALLPUTFLAG IN VARCHAR2,
S IN NUMBER,
X IN NUMBER,
T IN NUMBER,
R IN NUMBER,
V IN NUMBER ) RETURN NUMBER
IS
--
D1 NUMBER;
D2 NUMBER;
PI NUMBER := 3.141592653589793238462643;
RESULT NUMBER;
--
FUNCTION CND ( X NUMBER ) RETURN NUMBER
IS
--
L NUMBER;
K NUMBER;
A1 NUMBER := 0.31938153;
A2 NUMBER := -0.356563782;
A3 NUMBER := 1.781477937;
A4 NUMBER := -1.821255978;
A5 NUMBER := 1.330274429;
RESULT NUMBER;
--
BEGIN
--
L := ABS(X);
K := 1 / (1 + 0.2316419 * L);
RESULT := 1 - 1 / SQRT(2 * PI) * EXP(-POWER(L, 2) / 2)
* (A1 * K + A2 * POWER(K, 2) + A3 * POWER(K, 3)
+ A4 * POWER(K, 4) + A5 * POWER(K, 5));
IF ( X < 0 ) THEN
RESULT := (1 - RESULT);
END IF;
--
RETURN RESULT;
--
END CND;
--
BEGIN
--
RESULT := 0;
D1 := (LN(S / X) + (R + POWER(V, 2) / 2) * T) / (V * SQRT(T));
D2 := D1 - V * SQRT(T);
IF ( CALLPUTFLAG = 'C' ) THEN
RESULT := S * CND(D1) - X * EXP(-R * T) * CND(D2);
ELSIF ( CALLPUTFLAG = 'P' ) THEN
RESULT := X * EXP(-R * T) * CND(-D2) - S * CND(-D1);
END IF;
--
RETURN RESULT;
--
END;

CREATE OR REPLACE FUNCTION BLACKSCHOLES ( CALLPUTFLAG IN VARCHAR2,

S IN NUMBER,

X IN NUMBER,

T IN NUMBER,

R IN NUMBER,

V IN NUMBER ) RETURN NUMBER

D1 NUMBER;

D2 NUMBER;

PI NUMBER := 3.141592653589793238462643;

RESULT NUMBER;

FUNCTION CND ( X NUMBER ) RETURN NUMBER

L NUMBER;

K NUMBER;

A1 NUMBER := 0.31938153;

A2 NUMBER := -0.356563782;

A3 NUMBER := 1.781477937;

A4 NUMBER := -1.821255978;

A5 NUMBER := 1.330274429;

RESULT NUMBER;

BEGIN

L := ABS(X);

K := 1 / (1 + 0.2316419 * L);

RESULT := 1 - 1 / SQRT(2 * PI) * EXP(-POWER(L, 2) / 2)

* (A1 * K + A2 * POWER(K, 2) + A3 * POWER(K, 3)

+ A4 * POWER(K, 4) + A5 * POWER(K, 5));

IF ( X < 0 ) THEN

RESULT := (1 - RESULT);

END IF;

RETURN RESULT;

END CND;

BEGIN

RESULT := 0;

D1 := (LN(S / X) + (R + POWER(V, 2) / 2) * T) / (V * SQRT(T));

D2 := D1 - V * SQRT(T);

IF ( CALLPUTFLAG = 'C' ) THEN

RESULT := S * CND(D1) - X * EXP(-R * T) * CND(D2);

ELSIF ( CALLPUTFLAG = 'P' ) THEN

RESULT := X * EXP(-R * T) * CND(-D2) - S * CND(-D1);

END IF;

RETURN RESULT;

END;

Black-Scholes in Ruby by Michael Neumann, Germany

# one-to-one translation from Python example
# Cumulative normal distribution
def cnd(x)
a1, a2, a3, a4, a5 = 0.31938153, -0.356563782, 1.781477937, -1.821255978, 1.330274429
l = x.abs
k = 1.0 / (1.0 + 0.2316419 * l)
w = 1.0 - 1.0 / Math.sqrt(2*Math::PI)*Math.exp(-l*l/2.0) * (a1*k + a2*k*k + a3*(k**3) + a4*(k**4) + a5*(k**5))
w = 1.0 - w if x < 0
return w
end

def BlackScholes(callPutFlag, s, x, t, r, v)
d1 = (Math.log(s/x)+(r+v*v/2.0)*t)/(v*Math.sqrt(t))
d2 = d1-v*Math.sqrt(t)
if callPutFlag == 'c'
s*cnd(d1)-x*Math.exp(-r*t)*cnd(d2)
else
x*Math.exp(-r*t)*cnd(-d2)-s*cnd(-d1)
end
end

# one-to-one translation from Python example

# Cumulative normal distribution

def cnd(x)

a1, a2, a3, a4, a5 = 0.31938153, -0.356563782, 1.781477937, -1.821255978, 1.330274429

l = x.abs

k = 1.0 / (1.0 + 0.2316419 * l)

w = 1.0 - 1.0 / Math.sqrt(2*Math::PI)*Math.exp(-l*l/2.0) * (a1*k + a2*k*k + a3*(k**3) + a4*(k**4) + a5*(k**5))

w = 1.0 - w if x < 0

return w

end

def BlackScholes(callPutFlag, s, x, t, r, v)

d1 = (Math.log(s/x)+(r+v*v/2.0)*t)/(v*Math.sqrt(t))

d2 = d1-v*Math.sqrt(t)

if callPutFlag == 'c'

s*cnd(d1)-x*Math.exp(-r*t)*cnd(d2)

else

x*Math.exp(-r*t)*cnd(-d2)-s*cnd(-d1)

end

Black-Scholes in VB.NET By Marco Sturlese,

'// The Black and Scholes (1973) Stock option formula

Public Function BlackScholes(ByVal CallPutFlag As String, ByVal S As Double,
ByVal X _

As Double, ByVal T As Double, ByVal r As Double, ByVal v As Double) As
Double

Dim d1 As Double, d2 As Double

d1 = (Math.Log(S / X) + (r + v ^ 2 / 2) * T) / (v * Math.Sqrt(T))

d2 = d1 - v * Math.Sqrt(T)

If CallPutFlag = "c" Then

BlackScholes = S * CND(d1) - X * Math.Exp(-r * T) * CND(d2)

ElseIf CallPutFlag = "p" Then

BlackScholes = X * Math.Exp(-r * T) * CND(-d2) - S * CND(-d1)

End If

End Function

'// The cumulative normal distribution function

Public Function CND(ByVal X As Double) As Double

Dim L As Double, K As Double

Const a1 = 0.31938153 : Const a2 = -0.356563782 : Const a3 = 1.781477937

Const a4 = -1.821255978 : Const a5 = 1.330274429

L = Math.Abs(X)

K = 1 / (1 + 0.2316419 * L)

CND = 1 - 1 / Math.Sqrt(2 * Math.PI) * Math.Exp(-L ^ 2 / 2) * (a1 * K + a2 *
K ^ 2 + a3 * K ^ 3 + a4 * K ^ 4 + a5 * K ^ 5)

If X < 0 Then

CND = 1 - CND

End If

End Function

'// The Black and Scholes (1973) Stock option formula

Public Function BlackScholes(ByVal CallPutFlag As String, ByVal S As Double,

ByVal X _

As Double, ByVal T As Double, ByVal r As Double, ByVal v As Double) As

Double

Dim d1 As Double, d2 As Double

d1 = (Math.Log(S / X) + (r + v ^ 2 / 2) * T) / (v * Math.Sqrt(T))

d2 = d1 - v * Math.Sqrt(T)

If CallPutFlag = "c" Then

BlackScholes = S * CND(d1) - X * Math.Exp(-r * T) * CND(d2)

ElseIf CallPutFlag = "p" Then

BlackScholes = X * Math.Exp(-r * T) * CND(-d2) - S * CND(-d1)

End If

End Function

'// The cumulative normal distribution function

Public Function CND(ByVal X As Double) As Double

Dim L As Double, K As Double

Const a1 = 0.31938153 : Const a2 = -0.356563782 : Const a3 = 1.781477937

Const a4 = -1.821255978 : Const a5 = 1.330274429

L = Math.Abs(X)

K = 1 / (1 + 0.2316419 * L)

CND = 1 - 1 / Math.Sqrt(2 * Math.PI) * Math.Exp(-L ^ 2 / 2) * (a1 * K + a2 *

K ^ 2 + a3 * K ^ 3 + a4 * K ^ 4 + a5 * K ^ 5)

If X < 0 Then

CND = 1 - CND

End If

End Function

Black-Scholes in F# By Michael de la Maza

#light

// This code was transliterated from the OCAML code
// located here http://www.espenhaug.com/black_scholes.html

let pow x n = exp (n * log(x) ) 

let cnd x =
   let a1 =  0.31938153
   let a2 = -0.356563782
   let a3 =  1.781477937
   let a4 = -1.821255978
   let a5 =  1.330274429
   let pi = 4.0 * atan 1.0
   let l  = abs(x)
   let k  = 1.0 / (1.0 + 0.2316419 * l)
   let w  = ref (1.0-1.0/sqrt(2.0*pi)*exp(-l*l/2.0)*(a1*k+a2*k*k+a3*(pow k 3.0)+a4*(pow k 4.0)+a5*(pow k 5.0)))
   if (x < 0.0) then  w := 1.0 - !w
   !w

// call_put_flag: 'c' if call option; otherwise put option
// s: stock price
// x: strike price of option
// t: time to expiration in years
// r: risk free interest rate
// v: volatility
let black_scholes call_put_flag s x t r v =
   let d1=(log(s / x) + (r+v*v/2.0)*t)/(v*sqrt(t))
   let d2=d1-v*sqrt(t)
   let res = ref 0.0
   if (call_put_flag = 'c') then
      res := s*cnd(d1)-x*exp(-r*t)*cnd(d2)
   else
      res := x*exp(-r*t)*cnd(-d2)-s*cnd(-d1)
   !res

Example usage::

> black_scholes 'c' 60.0 65.0 0.25 0.08 0.3;;
val it : float = 2.133371862
> black_scholes 'p' 60.0 65.0 0.25 0.08 0.3;;
val it : float = 5.846285627

#light

// This code was transliterated from the OCAML code

// located here http://www.espenhaug.com/black_scholes.html

let pow x n = exp (n * log(x) )

let cnd x =

let a1 = 0.31938153

let a2 = -0.356563782

let a3 = 1.781477937

let a4 = -1.821255978

let a5 = 1.330274429

let pi = 4.0 * atan 1.0

let l = abs(x)

let k = 1.0 / (1.0 + 0.2316419 * l)

let w = ref (1.0-1.0/sqrt(2.0*pi)*exp(-l*l/2.0)*(a1*k+a2*k*k+a3*(pow k 3.0)+a4*(pow k 4.0)+a5*(pow k 5.0)))

if (x < 0.0) then w := 1.0 - !w

// call_put_flag: 'c' if call option; otherwise put option

// s: stock price

// x: strike price of option

// t: time to expiration in years

// r: risk free interest rate

// v: volatility

let black_scholes call_put_flag s x t r v =

let d1=(log(s / x) + (r+v*v/2.0)*t)/(v*sqrt(t))

let d2=d1-v*sqrt(t)

let res = ref 0.0

if (call_put_flag = 'c') then

res := s*cnd(d1)-x*exp(-r*t)*cnd(d2)

else

res := x*exp(-r*t)*cnd(-d2)-s*cnd(-d1)

!res

Example usage::

> black_scholes 'c' 60.0 65.0 0.25 0.08 0.3;;

val it : float = 2.133371862

> black_scholes 'p' 60.0 65.0 0.25 0.08 0.3;;

val it : float = 5.846285627

Black-Scholes in Objective-C/iPhone By Paul J. Sholtz

HEADER FILE/DECLARATION:

-(double)BlackSholes:(char)CallPutFlag: (double)S: (double)X: (double)T: (double)r: (double)v;
-(double)CND:(double)X;

IMPLEMENTATION:

#ifndef Pi 
#define Pi 3.141592653589793238462643 
#endif 

-(double)BlackSholes:(char)CallPutFlag: (double)S: (double)X: (double)T: (double)r: (double)v
{
	double d1, d2;

	d1=(log(S/X)+(r+v*v/2)*T)/(v*sqrt(T));
	d2=d1-v*sqrt(T);

	if(CallPutFlag == 'c')
		return S *[self CND:d1]-X * exp(-r*T)*[self CND:d2];	if(CallPutFlag == 'p')
		return X * exp(-r * T) * [self CND:-d2] - S * [self CND:-d1];

	// error flag; 
	[NSException raise:@"Call/Put Error" format:@"Option must be either a call or put"];
}
-(double)CND:(double)X
{
	double L, K, w ;

	double const a1 = 0.31938153, a2 = -0.356563782, a3 = 1.781477937;
	double const a4 = -1.821255978, a5 = 1.330274429;
	L = fabs(X);
	K = 1.0 / (1.0 + 0.2316419 * L);
	w = 1.0 - 1.0 / sqrt(2 * Pi) * exp(-L *L / 2) * (a1 * K + a2 * K *K + a3 * pow(K,3) + a4 * pow(K,4) + a5 * pow(K,5));

	if (X &lt; 0 ){ w= 1.0 - w; }
	return w;
}

INVOCATION (LOGGING ANSWER TO CONSOLE):
(models a call option, equity price 50, strike price 45, time to expiry 1/3 of a year, 8% risk free rate and 30% volatility)

	char flag = 'p';
	double S = 50.0;
	double X = 45.0;
	double T = 1./3.;
	double r = 0.08;
	double v = 0.3;

	double option_value = [self BlackSholes:flag :S :X :T :r :v];
NSLog(@"option value: %f",option_value);

HEADER FILE/DECLARATION:

-(double)BlackSholes:(char)CallPutFlag: (double)S: (double)X: (double)T: (double)r: (double)v;

-(double)CND:(double)X;

IMPLEMENTATION:

#ifndef Pi

#define Pi 3.141592653589793238462643

#endif

-(double)BlackSholes:(char)CallPutFlag: (double)S: (double)X: (double)T: (double)r: (double)v

{

double d1, d2;

d1=(log(S/X)+(r+v*v/2)*T)/(v*sqrt(T));

d2=d1-v*sqrt(T);

if(CallPutFlag == 'c')

return S *[self CND:d1]-X * exp(-r*T)*[self CND:d2]; if(CallPutFlag == 'p')

return X * exp(-r * T) * [self CND:-d2] - S * [self CND:-d1];

// error flag;

[NSException raise:@"Call/Put Error" format:@"Option must be either a call or put"];

}

-(double)CND:(double)X

{

double L, K, w ;

double const a1 = 0.31938153, a2 = -0.356563782, a3 = 1.781477937;

double const a4 = -1.821255978, a5 = 1.330274429;

L = fabs(X);

K = 1.0 / (1.0 + 0.2316419 * L);

w = 1.0 - 1.0 / sqrt(2 * Pi) * exp(-L *L / 2) * (a1 * K + a2 * K *K + a3 * pow(K,3) + a4 * pow(K,4) + a5 * pow(K,5));

if (X < 0 ){ w= 1.0 - w; }

return w;

}

INVOCATION (LOGGING ANSWER TO CONSOLE):

(models a call option, equity price 50, strike price 45, time to expiry 1/3 of a year, 8% risk free rate and 30% volatility)

char flag = 'p';

double S = 50.0;

double X = 45.0;

double T = 1./3.;

double r = 0.08;

double v = 0.3;

double option_value = [self BlackSholes:flag :S :X :T :r :v];

NSLog(@"option value: %f",option_value);

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