[Quantlib-dev] Finite differences and discrete dividends

[Joseph W. <jo...@co...>]

About two weeks ago, Luigi put in some unit tests for the finite 
difference method discrete dividend engine which failed the tests.  
After some work, I was able to modify the FD engine so that the results 
match the analytic formula which assumes that the value of the option is 
what it would be if the discounted values of the dividends were 
subtracted from the underlying.

So everything is good.....

Until I come across a paper by Haug that argues that the classic 
discrete dividend option formula is wrong.  This brings up the 
possibility that the original algorithm which failed the unit tests is 
actually the correct one.

The original quantlib algorithm backward evolves the price curve and if 
it encounters a dividend payout of $N, it shifts the price curve by N.

The new algorithm which matches the results in the analytic formula and 
the "classic dividend" formula, first calculates the discounted dividend 
payout and then it scales the price curve by a factor of (U+N)/U where U 
is the price of the underlying.

One of the implications of the original quantlib algorithm is that an 
option that pays out $5 on an underlying spot price of 100 will be 
valued differently than an option that pays out 5% on underlying spot 
price of $100.

So the question I have is does anyone have a reference to a recent paper 
talking about how to handle discrete dividends with finite differences.