Hi I'm trying to incorporate discrete fixed dividends in my binomial american option pricer. Initially I thought it was simply a question of subtracting the dividend from all the nodes at the correct point in time... however I just found out that this means that the tree doesn't recombine.My question: is it possible force the tree to recombine by taking some weighted average of the pairs of nodes? Or is it usual to just allow the tree to split? Or should I just make do with proportional dividends?Thanks in advance.

Another problem:I'm also trying to write a finite differences pricer. I'm using the Crank-Nicholson method to price a plain vanilla European call option... that way I can benchmark it against the exact analytic prices before moving on to more complex options.I'm having various problems with it and none of the books I have are any help. 1. How should I choose the number of timesteps relative to the number of steps in the price? Initially I set them equal and got terrible answers. Then I tried putting the number of price steps equal to the square root of the number of price steps and got much better prices. Is there an optimal choice?2. How should I choose the upper and lower limits of the mesh?Could anyone recommend a book which covers this in detail?Thanks

the standard technique is to subtract the pv of the divis up to the expiry of the option from the spot price and then use that adjusted price to evolve the tree. Then at each node, when checking for early exercise, add back the dividends from that node to the expiry to the stock price at the node.hth

QuoteOriginally posted by: jebusHi I'm trying to incorporate discrete fixed dividends in my binomial american option pricer. Initially I thought it was simply a question of subtracting the dividend from all the nodes at the correct point in time... however I just found out that this means that the tree doesn't recombine.My question: is it possible force the tree to recombine by taking some weighted average of the pairs of nodes? Or is it usual to just allow the tree to split? Or should I just make do with proportional dividends?Thanks in advance.You might be interested in:Back to Basics: a new approach to the discrete dividend problem Haug, Haug, and Lewis, Wilmott mag., September 2003. regards,

Take also a look at "efficient pricing of derivatives on assets with discrete dividends" by Vellekoop en Nieuwenhuis.I don't know where it is published though..

Hi, I am trying to use binomial tree to price options (European & American) with discrete dividends. Because the unit for time is year, will the price/greeks be correct around the ex-date? Or I have to do the time-step as day?

QuoteOriginally posted by: eye51Take also a look at "efficient pricing of derivatives on assets with discrete dividends" by Vellekoop en Nieuwenhuis.I don't know where it is published though..Efficient Pricing of Derivatives on Assets with Discrete DividendsM. H. Vellekoop and J. W. Nieuwenhuis Applied Mathematical Finance, 2006, vol. 13, issue 3, pages 265-284

QuoteOriginally posted by: daveangelthe standard technique is to subtract the pv of the divis up to the expiry of the option from the spot price and then use that adjusted price to evolve the tree. Then at each node, when checking for early exercise, add back the dividends from that node to the expiry to the stock price at the node.Hi Daveangel, if you drop by this thread again, could you detail with any formalized math. expression this step? Thanks!hth

Hi Bambi,You can find in in Hull, in the chapter about numerical methods. There is also an example the implementation.

Hi Eye51, which edition of the Hull please? Many thanks.

You'll also have to adjust the volatility, not only the underlying, for the dividends. Because only the ex-dividend part of the stock is going to fluctuate in the model, but the volatility you use applies to the full stock. This is a well-known flaw of discrete dividends and is well-described in Haug-Haug, already mentioned above by Alan.

Bambi,The chapter is in all editions of Hull. In the 6th edition, it's chapter 17.If you would use the method of Vellekoop, you do not need the adjustment villiger is talking about.