Re: [Quantlib-users] The reason of differences between `FDDividendAmericanEngine` of QuantLib 1.12 and `FdBlackScholesVanillaEngine` of QuantLib 1.18

[Shenze W. <she...@da...>]

Hi Klaus,

Thanks a lot for you explanations.

I made more calculations. It seems that the differences between Spot dividend model and Escrowed dividend model are not only for pathologic cases. And also a greater number of time steps and grid points do not help. The calculation results are attached. So I guess that there may be something goes wrong with Spot dividend model.

The difference between the two dividend model also causes another bug in impliedVolatility. Because for American options, FdBlackScholesVanillaEngine with Spot dividend model is always being used, when calculating ivol. Here is the issue I opened, https://github.com/lballabio/QuantLib/issues/850.

I think maybe it is necessary to take a closer look at the two dividend models.


Best,
Shenze
On Jun 25, 2020, 11:49 PM -0400, Klaus Spanderen <kl...@sp...>, wrote:
> please ignore my comment on "Observation 1 on Case 2", it is wrong,
>
> On Donnerstag, 25. Juni 2020 22:45:18 CEST Klaus Spanderen wrote:
> > Hi,
> >
> > thanks for sharing your results.
> >
> > W.r.t. your questions
> > 1. Douglas and Crank-Nicolson scheme are exactly the same for one-dimensional problems like the Black-Scholes equation. In higher dimensions operator splitting schemes like Douglas or Craig-Sneyd are better suited than Crank-Nicolson, hence there wasn't really a need to implement it (even though for the sake of completeness the Crank-Nicolson scheme has been added with the 1.18 release in C++).
> > 2. The spot dividend model is described e.q. in "Back to Basics: a new approach to the discrete dividend problem". People might argue that the spot dividend process is more realistic for path dependent options like barrier options or structured equity notes.
> > 3. As far as I know there is no general and meaningful algorithm for this problem, which is as easy as for Monte-Carlo.
> >
> > Observation 1 on Case 2. If I remember correctly then there was subtle difference between interest rate treatment for discrete dividents between the FDDividendAmericanEngine on the one side and AnalyticDividendEuropeanEngine,FdBlackScholesVanillaEngine on the other side.
> > Observation 2: For these pathologic cases the default number of S grid steps is too small. In general I'd use 500 or more S grid steps.
> >
> > best regards
> > Klaus
> >
> >
> >
> >
> > _______________________________________________
> > QuantLib-users mailing list
> > Qua...@li...
> > https://lists.sourceforge.net/lists/listinfo/quantlib-users
> >
>
>
>
>
>
>
> _______________________________________________
> QuantLib-users mailing list
> Qua...@li...
> https://lists.sourceforge.net/lists/listinfo/quantlib-users