equivalent of shell script's grep command in perl

There is actually a grep function in perl. It takes an expression or a block as the first argument and a list of strings as the second argument. So you could do this:

my @list = grep(/abcd/, (<>));

See also: grep - perldoc.perl.org

In your specific case you can use the block form to extract the price like this:

imp_vol | perl -e 'print grep { s/\s+Black Scholes Vol = ([-+]?[0-9]*\.?[0-9]+)/$1/ } (<>)'

If you want all "Black Scholes " like your grep would match

imp_vol -u $undr_price -s $str_price -p $price -t $mat -c $iscall | perl -ne 'print $1 if $_ =~ /Black Scholes .* = (\d+(?:\.\d+)?)/;'

"Black Scholes Vol" exactly

| perl -ne 'print $1 if $_ =~ /Black Scholes Vol = (\d+(?:\.\d+)?)/;'

Use Regexes

while (<>) {
    next if !/abcd/;
    # ...
}

Also, to replace cut, use capture groups, but I can't provide more code because I don"t know your data format.

To execute the command, you can use open to get a filehandle from which you can read its output. You can then use a single regular expression to match the line and extract the value. For example:

my $cmd = "imp_vol -u $undr_price -s $str_price -p $price -t $mat -c $iscall";
open (my $imp, '-|', $cmd) or die "Couldn't execute command: $!";

my $extracted;
while (<$imp>) {
    if (/Black Scholes Vol = (.*)/) {
        $extracted = $1;
    }
}
close $imp;

The parenthesis create a capture group which extracts the value into the special $1 variable.

If you're able to pipe input instead of having to execute the command within Perl, the following one-liner would suffice:

imp_vol ... | perl -ne 'print $1 if /Black Scholes Vol = (.*)/'