Re: Finite differences and discrete dividends

Posted by Ferdinando M. Ametrano-3 on Dec 23, 2005; 11:14am
URL: http://quantlib.414.s1.nabble.com/Finite-differences-and-discrete-dividends-tp4329p4330.html

Hi Joseph

On 12/22/05, Joseph Wang <[hidden email]> wrote:
> I come across a paper by Haug that argues that the classic
> discrete dividend option formula is wrong.
which paper are you referring to? I remember something published on
Wilmott Magazine, but I don't have access to it right now.

as for right/wrong...
formulas (and models) in widespread usage are never right or wrong in
my book, they are just used properly or improperly. Every trader is
used to twist input parameters to obtain reliable results out of
less-than-perfect formulas (and models)
:-)

> One of the implications of the original quantlib algorithm is that an
> option that pays out $5 on an underlying spot price of 100 will be
> valued differently than an option that pays out 5% on underlying spot
> price of $100.

this seems perfect to me. it's different if you have an announced
official discrete dividend of 5$ or if you have a generic estimated
dividend of 5%.

> The original quantlib algorithm backward evolves the price curve and if
> it encounters a dividend payout of $N, it shifts the price curve by N.
>
> The new algorithm which matches the results in the analytic formula and
> the "classic dividend" formula, first calculates the discounted dividend
> payout and then it scales the price curve by a factor of (U+N)/U where U
> is the price of the underlying.

The classic analityc formula you are referring to only handles 5%
dividend, finite differences can handle both 5% and 5$. The key point
in both cases is which vol a trader will use.

I personally would love FD to handle both percentage and absolute
dividends. Anway for short dated options the discrete case is probably
the most relevant.

I'm sure that pratictioners might add insightful comments...

ciao -- Nando

PS Merry Christmas everyone