Forums > Pricing & Modelling > American Option with Discrete Div

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 cquand Total Posts: 91 Joined: Sep 2007
 Posted: 2010-03-05 09:50 Good morning, My objective is to back out implied vol from option prices. I was using BS no matter if the options were European or American and it seemed pretty fine. Until I faced near dividend. It seems that most of the discrete div option models are for European option and apparently the backed out implied vol is still way out. I found two models for American Option with Discrete Div: 1. an Analytical Solution for Call only: The Implied vol seems in line but not for the put (was trying to tweak the Call/Put Parity but not sure it makes sense... vol for put is way out) 2. a non recombing tree approximation (therefore Call and Put): that seems fine, can imagine it slows and need work out the optimal accuracy/speed ratio (!) Please could you let me know what are your thoughts regarding the best practive?
 eye51 Total Posts: 196 Joined: Oct 2004
 Posted: 2010-03-05 11:45 Use recombining binomial trees :). You could either use the method as described in Hull or the one in M. H. Velekoop & J. W. Nieuwenhuis, "Efficient Pricing of Derivatives on Assets with Discrete Dividends", http://eprints.eemcs.utwente.nl/8116/01/VellekoopNieuwenhuisDividendsAppliedMathFin.pdf) When you use the method in Hull you should take care that the dividend influences the implied vol you will get (see Haug, Haug and Lewis "Back to basics"..", http://www.math.ku.dk/kurser/2005-1/finmathtowork/ODD.pdf) The method described in the paper of Vellekoop might seem difficult to implement, but once you know the trick it is quite simple. I prefer this method, because it does not suffer from the influence of dividend on implied vol. Also, you can use the trick to add all kind of funky stuff to you binomial tree. Peace means reloading your guns
 Dimatrix Total Posts: 539 Joined: May 2006
 Posted: 2010-03-05 13:06 While I do not have any clue of what to use, I know a current research paper on that topic which benchmarks against the method of Velekoop, have a look at Closed Formula for Options with Discrete Dividends Ctrl - L.
 eye51 Total Posts: 196 Joined: Oct 2004
 Posted: 2010-03-05 13:53 Hi Dimatrix, Thanks for the reference. I had not seen it before. Peace means reloading your guns
 cquand Total Posts: 91 Joined: Sep 2007
 Posted: 2010-03-05 17:07 Thanks very much your help guys
 hilss Total Posts: 55 Joined: Jun 2007
 Posted: 2015-10-12 17:47 Good morning all,I am trying to build the VELLEKOOP/NIEUWENHUIS tree. I do not fully understand the paper, but I understood the implementation (I think). However, I was considering extreme cases where Td (ex-div time) is one day away, and expiration is 5 months out. At that point, we will have very few points to interpolate from. This will cause bigger errors, correct?Any suggestions? I'm wondering if I could decrease delta_t to increase the number of nodes at Td. Then do another interpolation at some future time (Ti), where Td less than Ti Less than Texp So my tree will look more dense up to Ti, then back to "normal" after Texp. Would this work? Or am not thinking about this correctly?Thanks,hilss
 Baltazar Total Posts: 1760 Joined: Jul 2004
 Posted: 2015-10-13 08:17 Alternatively you could make the tree as if we were pricing that options a few days ago.Then you just take the option value at the middle node and at the correct time from your tree.The effect would be to have a wider tree at your div points. Qui fait le malin tombe dans le ravin
 hilss Total Posts: 55 Joined: Jun 2007
 Posted: 2015-10-13 18:40 Thank you Baltazar, that worked...hilss
 hilss Total Posts: 55 Joined: Jun 2007
 Posted: 2015-10-13 23:29 Does anybody have data on the convergence of the VELLEKOOP/NIEUWENHUIS model? I saw the table in their paper, but the data is limited. They don't show cases when we get very close to the x-div date.Is there a relationship between total variance (v * v * T) and the number of steps we should choose? What about the dividend value and dividend time?Example:S = 100K = 130v = 0.50T = 0.30r = 0.05n = 200d = 2Td = 0.10My non-recombining tree (my benchmark) is producing a Call price of 2.68the VN model is producing a Call price of 2.72Thanks,hilssP.S. I don't mind posting my VBA code if it's not against the forum policy.
 fomisha Total Posts: 27 Joined: Jul 2007
 Posted: 2016-05-09 21:54 here is a comprehensive review of different issues with dividend models and definitions of volatility:http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2634051
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