Discrete Dividends on Finite Differences

[Mndaweni, M. (Menzi)]

I have tried to implement discrete dividends when

pricing an option using finite differences scheme.

Has anyone been able to do this?

 

Menzi Mndaweni

Nedbank Capital

Equity Capital Markets

Quantitative Analyst

Tel (w):    +27 11 - 294 4516

Fax(w):    +27 11 - 759 7021

 

 

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[Luigi Ballabio]

On 03/16/2006 04:13:34 PM, Mndaweni, M. (Menzi) wrote:
> I have tried to implement discrete dividends when
> pricing an option using finite differences scheme.
> Has anyone been able to do this?

There are a few pricers for that in the library (see the sources inside  
ql/PricingEngines/Vanilla) but their reliability must still be  
assessed. Joseph, can you step in and comment?

Later,
        Luigi

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Hofstadter's Law:
         It always takes longer than you expect, even when you take
         Hofstadter's Law into account.

[Joseph Wang]

On Friday 17 March 2006 08:08，you write：
> On 03/16/2006 04:13:34 PM, Mndaweni, M. (Menzi) wrote:
> > I have tried to implement discrete dividends when
> > pricing an option using finite differences scheme.
> > Has anyone been able to do this?
>
> There are a few pricers for that in the library (see the sources inside
> ql/PricingEngines/Vanilla) but their reliability must still be
> assessed. Joseph, can you step in and comment?

Yes.  The default dividend vanilla fd engine in 0.3.12 produces results that
replicate the standard texts for European options.  Note that the default for
0.3.11 is different from the default for 0.3.11 which produces results quite
different from the standard textbooks.  The engine for 0.3.11 is included in
0.3.12 but you have to specifically ask for it.  Look in the header files for
that information.

There are three caveats.

1) The first is that the engines may be incorrect for American options.  The
problem is that the FD engines subtract the discounted value of the dividends
when issued, when in reality the amount that has to be discounted changes
over time.  This may (or may not) interfere with the step condition for
American options.  

2) The second is that I've read a paper by Haug that questions whether or not
the standard practice of subtracting the discounted value of dividends to
calculate the value of options is self-consistent and correct, and

see Back to Basics: A new approach to the discrete dividend problem.  Haug,
Haug and Lewis (it is available via google)

3) If that isn't bad enough, a lot has to do with the details of the dividend
issuance.  The lag between the time a dividend is declared and the time it is
issued changes things, as the fact that you aren't sure in advance when a
dividend will also be issued also changes things.  There is also a difference
between fractional and fixed dividends.

see "New Directions in Mathematical Finance" Paul Willmott ed.

Dr. Joseph Wang
China Derivatives Researcher