Sorry, that should be "for the returns of the underlying". On Tue, Apr 17, 2012 at 6:47 PM, Devon McCormick <devon...@gmail.com> wrote: > Looking at the formula, it appears to me that the normal distribution > is modeling a distribution of prices. In fact, this is explicitly > stated here - http://bradley.bradley.edu/~arr/bsm/pg04.html - in > assumption six: "returns on the underlying stock are normally > distributed". > > So the distribution is the model for the price of the underlying. > > On Tue, Apr 17, 2012 at 4:31 PM, KM Chakahwata > <kmchakahw...@first-derivative.com> wrote: >> sorry, I meant "expected option price", as of valuation date. for call, this >> would be Expected(S-K), which is the same as Expected(S)-K >> >> enjoy >> ken >> >> -----Original Message----- >> From: programming-boun...@jsoftware.com >> [mailto:programming-boun...@jsoftware.com] On Behalf Of KM Chakahwata >> Sent: 17 April 2012 20:39 >> To: 'Programming forum' >> Subject: Re: [Jprogramming] black-scholes and levy distribution >> >> the special form of Black-Scholes equation is based on the root stochastic >> differential equation that, through a series of so-called risk-neutral >> arguments leads to stock (or underlying) prices being lognormal. then we >> just find the present value (using risk free rate) of the expected stock >> price at expiration -- where the expectation is with respect to the >> lognormal distribution -- or normal when appropriate transformations are >> made from lognormal to normal (for mean and variance). >> >> now, given this, i dont know whether one can simply replace the cummulative >> distribution function "N" in BS formula with the appropriate Levy >> equivalent. i dont know that much about Levy, but i would be very pleasantly >> surprised if this is indeed the case -- but somehow i doubt it. i suspect >> you may have to go back to first principles and actually integrate the >> expectation equation somehow, assuming the risk neutral arguments still >> apply. >> >> anyone know for sure? >> >> enjoy >> ken >> >> -----Original Message----- >> From: programming-boun...@jsoftware.com >> [mailto:programming-boun...@jsoftware.com] On Behalf Of Devon McCormick >> Sent: 17 April 2012 19:51 >> To: Programming forum >> Subject: Re: [Jprogramming] black-scholes and levy distribution >> >> Raul - >> >> I've thought about this. Basically, you want to replace "N" (normal >> distribution) with "L" (Levy distribution) in the formula. This would >> require changing the "cnd" verb in McDonnel's essay to a "cld" >> (cumulative Levy distribution) verb, which gets right to the heart of >> the most complex piece of that code. >> >> I guess you've figured out how to write the Levy distribution verb? >> This is the crucial thing to get right - here's some graphs of it: >> http://en.wikipedia.org/wiki/L%C3%A9vy_distribution . >> >> What is "levychar"? Do you have some examples of using these verbs? >> >> Regards, >> >> Devon >> >> On Tue, Apr 17, 2012 at 2:04 PM, Raul Miller <rauldmil...@gmail.com> wrote: >>> I was reading >> http://triplehelixblog.com/2012/04/fractal-finance-a-rogue-mathematician%E2% >> 80%99s-search-for-answers/ >>> and then I was reading wikipedia's writeup on the levy distribution >>> (http://en.wikipedia.org/wiki/L%C3%A9vy_distribution) and then I was >>> poking around on jsoftware.com to find an implementation of erfc >>> >>> That gets me to here: >>> >>> require 'stats/distribs' >>> erfc=: erfc_pdistribs_ >>> >>> NB. m: location parameter (domain: y > m) >>> NB. n: scale parameter >>> levypdf=:2 :0 >>> (%: n%o.2) * ^@(n % 2 * m - ]) % 1.5 ^~ m -~ ] >>> ) >>> >>> levydist=:2 :0 >>> erfc@%:@(n % 2 * m -~ ]) >>> ) >>> >>> NB. no graph of this one -- it's complex -- not sure how to detect >>> stupid mistakes >>> levychar=:2 :0 >>> ^@((0j1*m)&* - 0j_2 %:@*n*]) >>> ) >>> >>> But I noticed this writeup on black-scholes: >>> http://www.jsoftware.com/papers/play193.htm and I got to wondering how >>> that would be rephrased if it used the assumptions that lead to the >>> levy distribution. >>> >>> Does anyone know how to approach this problem? >>> >>> Thanks, >>> >>> -- >>> Raul >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >> >> >> >> -- >> Devon McCormick, CFA >> ^me^ at acm. >> org is my >> preferred e-mail >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > Devon McCormick, CFA > ^me^ at acm. > org is my > preferred e-mail
-- Devon McCormick, CFA ^me^ at acm. org is my preferred e-mail ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
