Solver Black Scholes Option Pricing

Source code of 'Black Scholes Option Pricing'

This Solver (Black Scholes Option Pricing) was created by by PrateekJain(0)

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==section input
To calculate the price of a call/put option, please enter the following details:
Stock Price (S): $ *[input S=80]
Exercise Price (X): $ *[input X=100]
Risk free interest rate (r): *[input r=5]% per annum
Time to maturity(T): *[input T=1] years
Volatility (Annualized standard deviation) ({{{sigma}}}): *[input V=30]%
Yield (Dividend) to Maturity (y): *[input y=10]%

==section solution
perl

print "The Black Scholes Pricing formulas for European options are (where c is the call price and p is the Put price):
<center>
{{{c = Se^(-yT)N(d[1]) - Xe^(-rT)N(d[2])}}}

{{{p = Xe^(-rT)N(-d[2]) - Se^(-yT)N(-d[1])}}}

{{{d[1] = (ln(S/K)+(r + sigma^2/2)T)/(sigma*sqrt(T))}}}

{{{d[2] = d[1] - sigma*sqrt(T)}}}
</center>";

$r = $r/100;
$V=$V/100;
$y = $y/100;

$SX=$S/$X;
$logSX = ($SX**$SX - 1)/$SX;
$SXi = 1/$SX;
$logSXi = ($SXi**$SXi - 1)/$SXi;
$logSX = ($logSX-$logSXi)/2;

$d1=($logSX + ($r-$y+$V**2/2)*$T)/($V*sqrt($T));
$d2=$d1 - $V*sqrt($T);

if($d1 <= 1)
{
$Nd1 = 0.5 - 1/sqrt(2*3.14159265)*($d1-1/7*$d1**3);
}
else
{
$Nd1 = (1+$d1)*(1/sqrt(2*3.14159265)*exp(-$d1**2/2))/(1+$d1+$d1**2);
}

$Nd1 = 1 - $Nd1;

if($d2 <= 1)
{
$Nd2 = 0.5 - 1/sqrt(2*3.14159265)*($d2-1/7*$d2**3);
}
else
{
$Nd2 = (1+$d2)*(1/sqrt(2*3.14159265)*exp(-$d2**2/2))/(1+$d2+$d2**2);
}

$Nd2 = 1 - $Nd2;

$c = $S*exp(-$y*$T)*$Nd1 - $X*exp(-$r*$T)*$Nd2;
$p = $c - $S*exp(-$y*$T) + $X*exp(-$r*$T);

$c = sprintf("%.3f", $c);
$p = sprintf("%.3f", $p);
print " where N(x) is the cumulative normal distribution. ";
print "Thus the price of European options using these formulas would be: ";
print "Call Price (c) = $c ";
print "Put Price (p) = $p ";

==section output
c
==section check
 S=80 X=100 r=5 T=1 V=30 y=10 c=2.205