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

[Luigi B. <lui...@gm...>]

Hmm.  No, I would expect the result to change at least slightly.  Let me
check that.  Can you share the code you're using?

Luigi


On Tue, Jun 16, 2020 at 11:02 PM Shenze Wang <
she...@da...> wrote:

> Hi Luigi,
>
> Thanks a lot for the reply.
>
> I did not set the parameter `CashDividendModle` of the constructor
> `FdBlackScolesVanillaEngine` explicitly in my previous calculations.
>
> However, it seems that the parameter `CashDividendModle` does not affect
> the results at all.
>
> I calculated the prices of a bunch of American options with dividend
> yields with the engine `FdBlackScolesVanillaEngine` from QuantLib 1.18.
> The results from 'CashDividendModel cashDividendModel = Spot’ and the
> results from 'CashDividendModel cashDividendModel = Escrowed’ are
> *identical*, literally. I am using the Python wrap.
>
> Is this normal?
>
>
> Best,
> Shenze
>
> On Jun 16, 2020, 4:51 AM -0400, Luigi Ballabio <lui...@gm...>,
> wrote:
>
> Hello,
>     thanks for the analysis.
>
> There are people here which are more capable of answering than I am, but
> just to make sure that we're comparing equals to
> equals: FdBlackScholesVanillaEngine has two possible ways to handle
> dividends, and we should document this better.  One is the scale/shift
> model, and the other is the escrowed dividend model; you can choose the
> model by mans of an optional last parameter for the constructor (see <
> https://github.com/lballabio/QuantLib-SWIG/blob/master/SWIG/options.i#L1202
> >).
>
> Now, FDDividendAmericanEngine uses the escrowed dividend model, which I'm
> told is the one described in most texts.
> Instead, FdBlackScholesVanillaEngine uses by default the scale/shift
> model.  If you didn't set the model explicitly, this might be the reason
> for the differences.  Passing Escrowed as the model would cause the results
> to be closer.
>
> If you did that already, though, we'll have to look closer into the code.
>
> Hope this helps,
>     Luigi
>
>
>
> On Mon, Jun 15, 2020 at 10:01 PM Shenze Wang <
> she...@da...> wrote:
>
>> Hi,
>>
>> We are currently using `FD*D*ividend*A*mericanEngine` (denoted by *DA* in
>> following) of QuantLib 1.12. Since this engine is removed in QuantLib 1.16,
>> we’d like to switch to `*Fd*BlackScholesVanillaEngine` (denoted by *FD *in
>> following) of QuantLib 1.18. Before we do the switch, we’d like to know the
>> difference between these two engines (DA engine in QuantLib 1.12 and FD
>> engine in QuantLib 1.18) and what are the impacts on the pricing results.
>> We are using the Python version of QuantLib.
>>
>> I priced ~7000 options with different ivols, strikes, interest rates,
>> dividend yields with 3 engines: (a) *DA12* - `FDDividendAmericanEngine`
>> in QuantLib 1.12, (b) *FD12* - `FdBlackScholesVanillaEngine` in QuantLib
>> 1.12,  and (c) *FD18* - `FdBlackScholesVanillaEngine` in QuantLib 1.18.
>>
>> Here are some comparisons of the results.
>>
>> *(1)* The difference between FD18 and DA12 including two parts: the
>> difference between FD12 & DA12, and the difference between FD18 & FD12. The
>> difference between FD12 & DA12 is much greater than the difference between
>> FD18 & FD12, as shown in the following form. The form shows CDF of the
>> differences. The numbers in the form are the probability that the
>> difference is in a certain range.
>>
>>
>> *(2)* *FD12 vs DA12*. The option prices generated by FD12 is greater
>> than DA12 for in-the-money options, but lower for at-the-money and
>> out-of-the-money options. Compared to the analytical solutions, FD12 is
>> more accurate for at-the-money and out-of-the-money options, while DA12 is
>> more accurate for in-the-money options.
>>
>>
>>
>> *(3)* *FD18 vs FD12. *Though it is relatively small, there is still a
>> difference between FD18 and FD12, as shown in the following figure.
>>
>>
>>
>> So, my questions are:
>>
>>    1. Do the difference between FD12 & DA12 and the difference between
>>    FD18 & FD12 described above behave as expected?
>>    2. What’s the potential reasons for these differences?
>>
>> I know the answers to these questions could be very subtle, but we’d like
>> to understand the reasons for these differences, at least to some extent. I
>> also tried to dig into the C++ codes, but I am not familiar with the codes
>> and I do not know where to start. If you could provide some explanations or
>> point me the right directions, I would be super grateful.
>>
>> Thanks a lot.
>>
>>
>> Best Regards,
>> Shenze Wang
>>
>> DataDock Solutions
>> _______________________________________________
>> QuantLib-users mailing list
>> Qua...@li...
>> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>>
>