Finite differences and discrete dividends
Posted by Joseph Wang on Dec 22, 2005; 2:54pm
URL: http://quantlib.414.s1.nabble.com/Finite-differences-and-discrete-dividends-tp4329.html
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.