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

[Klaus S. <kl...@sp...>]

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
> 
> 
> 
> 
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