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

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

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