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package Finance::Options::Calc; |
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4492
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use strict; |
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use Carp; |
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use constant PI => 4 * atan2(1,1); |
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use vars qw(@EXPORT @ISA $VERSION $s $k $r $vol $t $d1 $d2 $nd1); |
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1210
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require Exporter; |
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$VERSION = 0.90; |
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@ISA = qw( Exporter ); |
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=head1 NAME |
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C - Option analysis based on different option pricing models. |
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=head1 SYNOPSIS |
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use Finance::Options::Calc; |
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print b_s_call(90, 80, 20, 30, 4.5); |
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print b_s_put (90, 80, 20, 30, 4.5); |
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print call_delta(90, 80, 20, 30, 4.5); |
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print put_delta(90, 80, 20, 30, 4.5); |
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print call_theta(90, 80, 20, 30, 4.5); |
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print put_theta(90, 80, 20, 30, 4.5); |
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print gamma(90, 80, 20, 30, 4.5); |
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print vega(90, 80, 20, 30, 4.5); |
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print call_rho(90, 80, 20, 30, 4.5); |
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print put_rho(90, 80, 20, 30, 4.5); |
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=head1 DESCRIPTION |
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b_s_call() subroutines returns theorical value of the call option based on |
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Black_Scholes model. The arguments are current stock price, |
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strike price, time to expiration (calender days, note this module |
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does NOT use business days), volatility(%), annual interest rate(%) in order. |
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b_s_put() subroutines returns theorical value of the put option based on |
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Black_Scholes model. The arguments are current stock price, |
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strike price, time to expiration (calender days, note this module |
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does NOT use business days), volatility(%), annual interest rate(%) in order. |
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call_delta() returns call delta. |
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put_delta() returns put delta. |
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Other methods are similar. |
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=head1 TODO |
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51
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more calculation models will be included. |
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53
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=head1 AUTHOR |
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Chicheng Zhang |
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chichengzhang@hotmail.com |
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=cut |
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61
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@EXPORT = qw(b_s_call b_s_put call_delta put_delta vega |
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call_rho put_rho call_theta put_theta gamma); |
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sub _variables { |
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croak "Not enough arguments.\n" unless $#_ == 4; |
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68
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## s -- current price |
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## k -- strike price |
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## t -- time remains |
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## vol -- volatility |
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## r -- interest rate |
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($s, $k, $t, $vol, $r) = @_; |
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$r /= 100; |
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$vol /= 100; |
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$t /= 365; |
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$d1 = (log($s / $k) + ( $r + $vol * $vol / 2 ) * $t) / ($vol * (sqrt $t)); |
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$d2 = $d1 - $vol * (sqrt $t); |
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$nd1 = exp( - $d1 * $d1 / 2 ) / sqrt( 2 * PI ); |
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} |
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sub call_delta { |
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_variables(@_); |
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return sprintf "%5.5f", _norm($d1); |
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} |
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sub put_delta { |
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_variables(@_); |
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return sprintf "%5.5f", _norm($d1) - 1; |
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} |
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93
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sub call_theta { |
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_variables(@_); |
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my $theta_c = - $s * $nd1 * $vol / (2 * sqrt($t)) - $r * $k * exp( - $r * $t ) * _norm($d2); |
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return sprintf "%5.5f", $theta_c / 365; |
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} |
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sub put_theta { |
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_variables(@_); |
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my $theta_p = - $s * $nd1 * $vol / (2 * sqrt($t)) + $r * $k * exp( - $r * $t ) * _norm(-$d2); |
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return sprintf "%5.5f", $theta_p / 365; |
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} |
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105
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sub call_rho { |
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_variables(@_); |
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my $rho = $k * $t * exp( - $r * $t ) * _norm($d2); |
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return sprintf "%5.5f", $rho / 100; |
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} |
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111
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sub put_rho { |
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_variables(@_); |
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my $rho = - $k * $t * exp( - $r * $t ) * _norm(-$d2); |
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return sprintf "%5.5f", $rho / 100; |
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} |
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117
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sub vega { |
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0
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_variables(@_); |
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my $vega = $s * sqrt($t) * $nd1; |
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5
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return sprintf "%5.5f", $vega / 100; |
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} |
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123
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sub gamma { |
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0
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_variables(@_); |
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my $gamma= $nd1 / ( $s * $vol * sqrt($t) ); |
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return sprintf "%5.5f", $gamma; |
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} |
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129
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sub b_s_call { |
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_variables(@_); |
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1
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4
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my $c = $s * _norm($d1) - $k * (exp (-$r*$t)) * _norm($d2); |
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return sprintf "%5.5f", $c; |
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} |
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135
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sub b_s_put { |
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_variables(@_); |
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1
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6
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my $p = $k * (exp (-$r*$t)) * _norm(-$d2) - $s * _norm(-$d1); |
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1
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return sprintf "%5.5f", $p; |
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} |
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141
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sub _norm { |
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143
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my $d = shift; |
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my $step = 0.01; |
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my $sum = 0; |
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my $x = -5 + $step / 2; |
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148
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while ( ($x < $d) && ($x < 4) ) |
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{ |
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5350
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6816
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$sum += exp(- $x * $x / 2) * $step; |
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5350
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17509
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$x += $step; |
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} |
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return $sum / sqrt(2 * PI); |
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} |
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1; |
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