# インプライド・ボラティリティ Implied Volatility
# 引数 原資産価格 権利行使価格 残存期間(日) 安全資産利子率(%) 原資産利回り(%) オプションの現在価格 ($Price, $Strike, $CurrentMaturity, $RiskFreeRate, $DividendYield, %OpPrice)
# 戻り値 hash {'iv'}->({'call'} {'put'}) (%iv)
sub IV{
	my ($Price, $Strike, $CurrentMaturity, $RiskFreeRate, $DividendYield, %OpPrice) = @_;
	my %iv = ();
	my $Year = 365;
	my $pi = atan2(1, 1) * 4;
	my $SqrtCurrentMaturity = 0;
	$CurrentMaturity = $CurrentMaturity / $Year;
	$SqrtCurrentMaturity = sqrt($CurrentMaturity);
	$Volatility = $Volatility / 100;
	$RiskFreeRate =  $RiskFreeRate / 100;
	$DividendYield = $DividendYield / 100;
	
	# 計算
	my @op_price = ($OpPrice{'call'}, $OpPrice{'put'});
	my @tmp = ();
	for(my $i = 0; $i <= 1; $i++){
		my $Accuracy = 1.0e-6;
		my $diff = 1;
		my $vega = 0;
		my $t_op_price = 0;
		my $vo = (abs(log($Price / $Strike) + ($RiskFreeRate * $CurrentMaturity)) * 2 / $CurrentMaturity) ** 0.5;
	
		while(abs($diff) > $Accuracy){
			my $num1 = log($Price / $Strike);
			my $num2 = ($RiskFreeRate - $DividendYield + (($vo * $vo) / 2)) * $CurrentMaturity;
			my $den = $vo * $SqrtCurrentMaturity;
			my $d1 = ($num1 + $num2) / $den;
			my $d2 = $d1 - ($vo * $SqrtCurrentMaturity);
			my $nd1 = exp(-($d1 * $d1) / 2) / sqrt(2 * $pi);
	
			if($i == 0){
				# Call
				my $call_d1 = &NORMDIST($d1);
				my $call_d2 = &NORMDIST($d2);
				$t_op_price = (exp(-($CurrentMaturity * $DividendYield)) * ($Price * $call_d1)) - ($Strike * exp(-($CurrentMaturity * $RiskFreeRate)) * $call_d2);
			}else {
				# Put
				my $put_d1 = &NORMDIST(-$d1);
				my $put_d2 = &NORMDIST(-$d2);
				$t_op_price = ($Strike * exp(-($CurrentMaturity * $RiskFreeRate)) * $put_d2) -(exp(-($CurrentMaturity * $DividendYield)) * ($Price * $put_d1));
			}
			$diff = $op_price[$i] - $t_op_price;
			$vega = $Price * exp(-($CurrentMaturity * $DividendYield)) * $nd1 * $SqrtCurrentMaturity;
	
			if($vega == 0){
				$vo = "Illegal division by zero";
				last;
			}
	
			$vo = $vo + ($diff / $vega);
		}
	
		$tmp[$i] = $vo;
	}
	
	# IV
	$iv{'iv'}->{'call'} = $tmp[0];
	$iv{'iv'}->{'put'} = $tmp[1];
	
	return %iv;
}