Talk:Binomial options pricing model

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[edit] 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)

[edit] 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)

[edit] 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 Se ^{− qt}

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}

(Sorry for the confusing look of it, but I couldn't quite get the syntax of the math parser)

Douglas Robinson 21:43, 29 November 2006 (UTC)

I think your approach is a little off - you are using stock price (S) where you should be using option prices (C). Start with two trees, one filled with stock prices (S), the other with option prices (C). The stock prices are easy, base node is just S(0). Next step has Su and Sd. Third step has Suu, S(0) and Sdd, etc. Now, start filling in the option tree from back to front. The last step is also easy, just calculate expiration value of the option for each stock price from the stock tree. Next, go back one time step in the option tree using the binomial formula. However, use the values from the option tree, i.e.

Ronnotel 21:53, 29 November 2006 (UTC)

Okay,

I definitely have been approaching the model in the wrong way. Thanks for clearing that up for me. But the formula still has that weirdness to it.

If you start with

You can continue with:

(going to try out this math parser again... had a nice image of the equation and working out but I don't see how to upload it)

Douglas Robinson 15:09, 30 November 2006 (UTC)

I think I see a problem, please note that C_u is not the same as Cu. C_u can only be calculated through the backward induction step described above. Again, I would strongly encourage you to get ahold of either of the references I mentioned - going off this article alone is going to be a tough journey. Ronnotel 15:16, 30 November 2006 (UTC)