Finite differences and discrete dividends
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Finite differences and discrete dividends
 
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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. |
Re: Finite differences and discrete dividends
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Hi Joseph
On 12/22/05, Joseph Wang <[hidden email]> wrote: > I come across a paper by Haug that argues that the classic > discrete dividend option formula is wrong. which paper are you referring to? I remember something published on Wilmott Magazine, but I don't have access to it right now. as for right/wrong... formulas (and models) in widespread usage are never right or wrong in my book, they are just used properly or improperly. Every trader is used to twist input parameters to obtain reliable results out of less-than-perfect formulas (and models) :-) > 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 $100. this seems perfect to me. it's different if you have an announced official discrete dividend of 5$ or if you have a generic estimated dividend of 5%. > The original quantlib algorithm backward evolves the price curve and if > it encounters a dividend payout of $N, it shifts the price curve by N. > > The new algorithm which matches the results in the analytic formula and > the "classic dividend" formula, first calculates the discounted dividend > payout and then it scales the price curve by a factor of (U+N)/U where U > is the price of the underlying. The classic analityc formula you are referring to only handles 5% dividend, finite differences can handle both 5% and 5$. The key point in both cases is which vol a trader will use. I personally would love FD to handle both percentage and absolute dividends. Anway for short dated options the discrete case is probably the most relevant. I'm sure that pratictioners might add insightful comments... ciao -- Nando PS Merry Christmas everyone |
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I agree with Nando. We prefer $5 where
we can and it is actually very important to do it in certain cases.
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