Kristian Moe wrote: > > Let me start off by saying that I am not a statistics wiz; I've taken > an introductory college stat class, and that is about it. So if I mix > up terms here, bear with me. I'm working on a finance thesis, focusing > on options and value at risk. > > My problem is as follows: I am using a discrete pricing model > (binomial tree), and I have a number of possible outcomes with > corresponding probabilities. I.e. > > Result Prob Cum > 4735 0,0080 0,0080 > 2522 0,0530 0,0610 > 1343 0,1537 0,2147 > 715 0,2548 0,4695 > 381 0,2640 0,7335 > 203 0,1750 0,9085 > 108 0,0725 0,9810 > 58 0,0172 0,9982 > 31 0,0018 1,0000 > > From these values it is easy to draw a nice and smooth curve in Excel, > showing the distribution of the outcomes fairly exact (using scatter > plot with lines). Now I want an estimate of, say, the 5th percentile > of the outcomes. It is of course possible to use the cumulative > probability and get a "linear" eastimate. I am wondering whether > anyone can think of a more exact and elegant way of doing this? Is > there any statistics plug-ins that could be helpful? Any help would be > greatly appreciated.
Your problem is really one of numerical analysis more than statistics. You could use something like Simpson's Rule ( http://mathworld.wolfram.com/SimpsonsRule.html ) if your data were evenly spaced, which is isn't, and this only works if you have 3 or more points of your distribution at percentiles less than that in which you're interested (in the case you show you only have one for the 5th percentile, for instance). You could fit your data with cubic splines ( http://mathworld.wolfram.com/CubicSpline.html ) and integrate the resulting polynomial functions (if you remember calculus). Unlike Simpson's Rule, I don't know what the error characteristics of such a scheme are, but probably someone has studied that question. I'm sure there are packages that one could use to solve your problem using an approach like cubic splines (I imagine I could do it in Mathcad which sits on my disk), but I don't know of any that would be quick and easy (meaning just entering the data on a spread sheet and clicking on a single command). Maybe someone else here has a good solution, or you could try posting your question to sci.math.num-analysis. Regards, Russell . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
