Re: impliedVolatility always throws exception instead of 0 or 1

Posted by Ferdinando Ametrano-4 on
URL: http://quantlib.414.s1.nabble.com/impliedVolatility-always-throws-exception-instead-of-0-or-1-tp7284p7285.html

On Tue, Mar 24, 2009 at 5:11 PM, Grant Birchmeier
<[hidden email]> wrote:
> I have a large set of options that I'm running this on; some of them
> are at parity, which implies volatility=0.
< [...]
> 3) data values:
>            double underly = 3.505;
>            double strike = 2;
>            double rate = .00445;
>            double value = 1.505;
>            QuantLib.Date todaysDate = new QuantLib.Date(1,
> QuantLib.Month.March, 2009);
>            QuantLib.Date maturityDate = new QuantLib.Date(1,
> QuantLib.Month.May, 2009);

from the value you provide I guess an American call option on a
non-dividend-paying stock (non-dividend-paying in 20090301-20090501).
Risk Free rate is 0.445%.

It is never optimal to exercise such an option before the expiration
date, so it is worth as much as the European equivalent.
The European one is worth 1.5065 with 0% volatility and more as the
volatility increase: so it is not possible to find an implied vol for
a lower value such as 1.5050.

Anyway there are some numerical stability issues for *_VERY_* deep in
the money option, which are not hard to imagine given the lack of
sensitiveness to volatility.

You can verify these statements using a fairly recent QuantLibXL with
the attached spreadsheet

ciao -- Nando

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