Talk:Binomial options pricing model
Model practicality
I reverted a change by 59.162.216.53 that claimed the binomial model is impractical. This is not true. By in large, the binomial model is used by practioners for a variety of reasons, mostly having to do with accuracy. As a developer of quantitative option pricing models, I have a fairly broad exposure to this issue and have yet to come across a serious option trader relying on the Black-Scholes model for actual trading. Ronnotel 13:25, 27 September 2006 (UTC)
- Agreed. Plus what else do you use for Bermudan options (other than simulations and Finite Difference methods of course... ☺) Fintor 15:31, 28 September 2006 (UTC)
Discrete Dividends
I believe most practical binomial models use discrete dividends rather than a continuous dividend yield. Using a continuous dividend yield can result in significant mis-pricing at or near dividend dates. Any objections to changing the formula to reflect this? Ronnotel 16:55, 28 November 2006 (UTC)
- Why not show both formulae - with commentary as to differences? Fintor 17:49, 28 November 2006 (UTC)
Issues with the formula
I was using this article as a guideline for constructing a simple binomial model for valuing a stock option and came across an interesting problem/issue/quirkiness/something. I would get all my values do up the formula and I realized that when I changed the value for the volatility of the stock the end result did not change at all. Not even by the lowliest of decimal points. After reducing the formulae for the binomial value and the probability, p, I found out why.
The formula for the binomial value given in the ariticle is equivalent to
where:
S is the current price of the underlying
q is the dividend yield
t is the time step
(I hope I've given the correct key, all the variables above correspond to those in the article).
Why then, would the formula and the model require so much information if you only really need these three things? Is there a mistake somewhere in there maybe?
Or am I just making things up?
Douglas Robinson 18:28, 29 November 2006 (UTC)
- Doug, I'll take a look at the formula and see what can be done. In the mean time, check and see if you have access to a copy of Black-Scholes and Beyond by Neil Chriss or Option, Futures and Other Derivatives by John Hull. Both provide excellent, implementable algorithms. Ronnotel 18:50, 29 November 2006 (UTC)
- Um, the probability of an up (and down) transition incorporates the volatility. Go back and check how you are calculating your transition probabilities. But you should still try to get ahold of one of both of these references. Ronnotel 18:54, 29 November 2006 (UTC)
Binomial Formula
=pSu+(1-p)Sd)/(e^{rt})
=S(p({u-d}/{e^{rt}})+d/e^{rt})
=S({e^{(r-q)t+sigma*sqrt{t}}-1}/{e^{2sigma*sqrt{t}}-1}(e^{sigma*sqrt{t}-rt}-e^{-sigma*sqrt{t} -rt})=d/{e^{rt}})
=S({e^{-qt+2*sigma*sqrt{t}}-e^{-qt}}/{e^{2*sigma*sqrt{t}}-1}
=Se^{-qt}({e^{2*sigma*sqrt{t}}-1}/{e^{2*sigma*sqrt{t}}-1})
=Se^{-qt}