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Need some help!

I have calculated the theoretical price of an index option using BS and Binomial models and are now comparing the three. While BS and Binomial have approximately the same value, market price is way off. The Option is an European index option and assuming no dividends.

The difference between Market and BS/binomial should stem from binomial assuming markets are perfect (no commissions, bid-ask, etc)

BS assumes constant risk free rate and volatility. Other problems are estimation of volatility and that BS assumes no large shifts.

Can you think of any other reasons why they are different? The reason I am asking is that I feel market and the theoretical is too far apart. Binomial and Bs differ slightly from each other, but that is probably because of the number of steps I have used.

Thanks for your help. Scrolled through this site now and its nice of the contributors to help all the random people. Hopefully I can contribute some day as well!

Steven

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Please keep in mind. There is a big difference between Euro options and American options. European options cannot be exercised until the EXACT day of expiration. As opposed to American options which can be exercised on or any day before expiration. –  Kirill Fuchs Jun 19 '12 at 20:02
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2 Answers

Congratulations! You've found what's known in the biz as "an opportunity". If you do invest in options based on Black-Scholes and binomial models, and assuming you've done your math right, then all you need do now is buy options, or set up an option strategy, such that you profit as the theoretical and the real move toward each other.

Of course, that's assuming there isn't a couple of big players, or lots of little ones, that know something you don't, and that doesn't show up in the mathematical models.

For instance, say the math on the options on the French CAC say they should be worth X, but they're trading for X-98%. Now, that would be a perfect time to go long the CAC options, and you do. Then you turn on the television, and discover there's a whopping great starship spinning lazily over Paris, the alien operators of which have demanded the French Secret to the Greatest Bearnaise Sauce, or face Obliteration. To which the french, choosing a terrible time to change their stripes, have collectively replied with an unyielding 'Non!', and a stiffened middle finger. And the next day your options go to X-99%.

In all seriousness, the mathematical models are alluring, but they can also be blinding when taken solely by themselves. You also have to do hard risk analysis, know the ways of the underlying security, the emotions of the herd, and so on. But, if you do all that, then from time to time you may find yourself in possession of an opportunity, as you may be now, to make a big fat pile of cash for yourself.

Also: if this is the case, and if this fits within your preplanned strategy, then don't let a rare opportunity pass you by while you lock up with analysis paralysis because "it just couldn't be so". The fact is it can be so -- efficient market theory not withstanding, the market spends most of it's time hieing off in one dang fool direction or another. It's only efficient on average -- and that's a figure generally seen reflected in the market price only momentarily and on the perpendicular.

All of which, by the way, should not be taken as a recommendation on my part, to any action or inaction. Anything you do is solely your responsibility. You're on your own, win or lose. On your head be it, as they say. That said, if does work out, I wouldn't say no to a nominal 10% motivational fee.

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There is a reason, there is a math error in the derivation of Black-Scholes and that error may be in your binomial as well. This is the reason for the large difference between reality and the models. See http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1678726

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