File Coverage

blib/lib/Math/Random/Normal/Leva.pm

Criterion	Covered	Total	%
statement	28	32	87.5
branch	4	6	66.6
condition	4	5	80.0
subroutine	6	7	85.7
pod	2	2	100.0
total	44	52	84.6

package Math::Random::Normal::Leva;
use strict;
use warnings;

our $VERSION = "0.03";

use Exporter qw(import export_to_level);
our @EXPORT_OK = qw(gbm_sample random_normal);

use Math::Random::Secure qw(rand);

use Carp qw(confess);

=head1 NAME

Math::Random::Normal::Leva - generate normally distributed PRN using Leva method

=head1 VERSION

This document describes Math::Random::Normal::Leva version 0.02

=head1 SYNOPSIS

    use Math::Random::Normal::Leva;
    my @normal = map { random_normal() } 1..1000;

=head1 DESCRIPTION

Generates normally distributed pseudorandom numbers using algorithm described
in the paper "A Fast Normal Random Number Generator", Joseph L. Leva, 1992
(L)

=head1 FUNCTIONS

=cut

=head2 random_normal($rand)

Returns a random number sampled from the normal distribution.

=over 4

=item I<$rand>

is the value of the stock initially

=cut

# This algorithm comes from the paper
# "A Fast Normal Random Number Generator" (Leva, 1992)

sub random_normal {
    my $rand = shift || \&rand;
    my ( $s, $t ) = ( 0.449871, -0.386595 );    # Center point
    my ( $a, $b ) = ( 0.19600,  0.25472 );

    my $nv;
    while ( not defined $nv ) {
        my ( $u, $v ) = ( $rand->(), 1.7156 * ( $rand->() - 0.5 ) );
        my $x = $u - $s;
        my $y = abs($v) - $t;
        my $Q = $x**2 + $y * ( $a * $y - $b * $x );
        if ( $Q >= 0.27597 ) {
            next if ( $Q > 0.27846 || $v**2 > -4 * $u**2 * log($u) );
        }
        $nv = $v / $u;
    }

    return $nv;
}

=head2 gbm_sample($price, $vol, $t, $r, $q, $rand)

Generates a random sample price of a stock following Geometric Brownian Motion after t years.

=over 4

=item I<$price>

is the value of the stock initially

=item I<$vol>

is the annual volatility of the stock

=item I<$t>

is the time elapsed in years

=item I<$r>

is the annualized drift rate

=item I<$q>

is the annualized dividend rate

=item I<$rand>

custom rand generated if not passed will use Math::Random::Secure::rand

=back

note: all rates are taken as decimals (.06 for 6%)

=cut

sub gbm_sample {
    my ( $price, $vol, $time, $r, $q, $rand ) = @_;

    confess(
        'All parameters are required to be set: generate_gbm($price, $annualized_vol, $time_in_years, $r_rate, $q_rate)'
    ) if grep { not defined $_ } ( $price, $vol, $time, $r, $q );

    return $price *
      exp( ( $r - $q - $vol * $vol / 2 ) * $time + $vol * sqrt($time) * random_normal($rand) );
}

1;

__END__