can somebody outline pro and cons using one factor CRR binomial tree model against Bjerksund&Stensland approximation to price index options (american style) with low or zero dividends.thanks.

Pro: CRR can be as accurate as desired if adapted appropriately.Con: Accuracy takes computation time ...and how good is your volatility projection anyway?

I believe my vol projection is quite good, but if I use CRR for long time to expiry option with low dividends my deep ITM put options prices looks strange. Now I am looking for alternative model to test this behaviour. Any suggestions?

NikkiThese are known problems in general. Some people use finite difference: they are robust and have been around for the last 200 years!http://www.datasim-component.com/financ ... sBiniomial and trinomial are special finite diference, but there are others in this family, some of which are relly robustHave a lot at the articles and examine new horizons

QuoteOriginally posted by: nikkiI believe my vol projection is quite good, but if I use CRR for long time to expiry option with low dividends my deep ITM put options prices looks strange. Now I am looking for alternative model to test this behaviour. Any suggestions?There are ways of improving CRR trees, but they can become complex. If you want to work only with the (relatively simple) CRR trees, then you can work to a desired accuracy by iteration and interpolation/extrapolation (averaging even/odd time-steps and extrapolating doubled time-steps, for instance). You can verify your interpolation/extrapolation scheme by comparing European CRR prices to Black-Scholes. Experimenting with modelling the error by something like {a+b(-1)^n}/n, for instance (error decreases with time-steps n and oscillates for even/odd) should give you some idea how to make these interpolations and extrapolations.Here is a semi-empirical semi-theoretical iteration algorithm I once worked out to compute the price P to an accuracy delta:1. Compute intrinsic value I (assumes vol = 0).2. Choose a starting even # time-steps m.3. Compute CRR binomial value B_m.4. If abs(B_m - I) < 0.5*delta then use P = B_m. Otherwise5. Compute B_(m-1).6. Compute M_m = 0.5*{B_{m-1) + B_m}7. If abs(B_(m-1) - B_m) < delta or abs(M_m - I) < 0.5*delta then use P = M_m. Otherwise8. If on first loop go to 10. Otherwise9. If abs(M_m - E_m) < delta use P = M_m. Otherwise10. Compute B_2m and extrapolate E_2m = 2*B_2m - B_m 11. If abs(E_2m - M_m) < delta then use P = E_2m. Otherwise12. Double m (so that B_2m and E_2m now become B_m and E_m) and go back to step 5.I may have modified this a little in my actual code, but I haven't got the time to check now. Any way you should get the idea.If you need to work out a complete chain, rather than a single strike, you can store the price trees you have already computed and re-do only the back traversal as needed.

the best way to improve on CRR trees is not to start with themthe best choice of parameters for the binomial tree are those suggested by leisen and reimer - best place to look is entry number 5 from a google search on their names - efficient computation of option price sensitivities for options of american style by wallner and wystup

QuoteOriginally posted by: spursfanthe best way to improve on CRR trees is not to start with themthe best choice of parameters for the binomial tree are those suggested by leisen and reimer - best place to look is entry number 5 from a google search on their names - efficient computation of option price sensitivities for options of american style by wallner and wystupVery few questions ever have such a neatly packaged answer. The phrase "horses for courses" comes to mind. The way I look at it is this:If nikki is simply looking to test accuracy of CRR, then yes this is a way to compare, if an appropriate convergence test is used for the LR tree as well as the CRR tree, since LR trees converge quicker than CRR. But it's much quicker to compare European CRR to BS if you want to test a convergence algorithm for CRR and you already have CRR code, but not LR code. Indeed, if you can't get your CRR tree to converge, then there is probably an error in it somewhere and simply modifying it to an LR tree won't make any difference.As regards using LR instead of CRR, then it should be noted that LR requires a separate price tree for each strike, so it may not be the most efficient method for real-time computation of a complete constant volatility chain. (If one has an IV smile, however, then this is a moot point, but this begs the question of where the IV smile comes from.) Depending on future objectives, it may not be worth the time needed to understand and code another constant volatility method. If nikki's interest is purely in the optimal tree structure for an American option where each strike has a different constant volatility and has no interest in exotics or in non-constant volatility, then yes, LR is the way to go. If, on the other hand, nikki expects to branch out into volatility models and exotics then ensuring convergence of CRR first is as good a place as any to start out.

Here are some more general thoughts about diffusion trees that should probably go in a separate thread, but since spursfan has introduced the issue of optimal convergence I'll put them here.There are two fundamentally different approaches:1. Design a separate optimal tree for each contract that depends on the parameters of the derivative and assumes a constant volatility for each such parameter. (E.g. Leisen-Reimer for American options with a pre-determined strike-dependent volatility smile.)2. Design a single underlying tree using a real volatility model and a generalized convergence algorithm that can be used for multiple derivative types each with differing parameters merely by modifying the backwards traversal.Of course, there can be other hybrids of these two approaches. CRR is the common baseline. How you develop from there depends on which approach is most convenient for your needs.---------------Gunners fan

point taken as regards LR needing separate trees for each strike but given proper convergence and extrapolation it must get close to CRR efficiency in total even with say 10-20 different strikes - an LR tree with 31 steps can give a lot of the accuracy you need - and, yes of course, we're only in a BS world