Discussion in 'Options' started by TraderGreg, Jul 6, 2008.
Anyone know where the options pricing formula is or where I can get it?
there is no such thing as THE option formula.
There are several for several products: options on fx, futures, equites or bonds get priced through a different formula. Even for one product there are several formula's: these are model trying to reflect reality with each one of them having limits imposed on them, nothing more.
For equity-options the old basic formula is Black-and-Sholes which is based on a lognormal distribution of prices. This lognormal distribution cannot really be obtained with a simple mathematical equasion but needs some working on in itself. You can find a way around this in a book like "options as a strategic investment'" by McMillan where he gives you the mathematical solution for this problem. Put it in a spreadsheet and you have your prices.
However ... Black-and-Sholes has several limits and probably no market-maker will use it to price his options anymore, but it's a good first start and with some adjusting you get decent prices. At least if you manage to guess volatility first and if you take skew of volatility into account. As you can see it's just a model ...
The Black & Scholes formula is still used and likely will continue to be used for pricing European options and the Euro currency, AFAIK.
So in this model what's substituted for the strike price if I wanted to forecast volatility in a stock, commodity, stock future or index future? The equilibrium level of a set period's trading range? Or is that the strike price?
Converting a risk-free interest rate into an annualized compounded rate as I gather is taken from one of three sources: the rate of the Dollar/Euro pair, the 10 Year T-Bond or the 30 Year T-Bond. Market Price intraday, the close or an EMA average true range for current price is easy enough. A weighted mean of dividend yields for x periods is readily available. Even if you are solely using a spreadsheet, what are you using for a strike price? More importantly, how do you calculate it where it's not option equity dependant?
I was an option market maker 10 years ago, even then almost nobody used Black and Sholes anymore. For currencies you can't really use the classic Black and Sholes as two intrest rates are needed.
For intrest rates the intrest rate is used for the remaining time of the option, but that can differ from market participant to market participant or whether you are long or short.
I don't follow where you are heading with the rest of your post, no moving average is used or true range. Certainly no weigthed avarage of dividends either. I don't get your problem with strike price either: that's a given, that shouldn't be calculated.
Somewhere, someone's that not a generality skirting, protruding blow-hard wind gash will answer my question.
Oh a dividend isn't discounted huh? Was that a later addition after times you were a market maker but now frequent trading boards for the terminally bored, underappreciated and minimally wealthy? lol
it's obvious you talk big, but you know shit ...
If black and sholes is no longer used to price options, is there any other model that can give me good valuations?
all these models have their limitations, these are especially important for market makers. They prefer more sophisticated stuff. You can still use B&S, but prices won't be perfect, you have to know how to adapt and realise that a lot of the input/output will be estimates.
There is no such thing as THE exact theoretical price of an option.
Black-Scholes *is* still used for European style options (can only be exercised on expiration day). On American exchanges, index options are prime examples of Euro-style.
American-style options (can be exercised any time) are generally priced using the Bjerksund-Stensland formula, but that won't help you much. It's more complicated than Black-Scholes and has certain implementation complexities that you can't ignore. It's not a plug and play like Black-Scholes.
Even worse, I can't abbreviate the formula to BS because they're both abbreviated the same.
There are also algorithms called binomial and trinomial approximations that can be used too, but I don't know how widespread their use is.
There, now you have some good Google search terms for further research.
For implied volatility there're the B&S model, GARCH model, and Binomial Model.
Most Quants use GARCH-based models over a broad range of sectors and if there hasn't been a liking to an equation improving on the B&S model, which, is prefered if you want to get close to accuracy and real-time, then traders gravitate toward either the Stochastic Volatility model or a larger period Binomial Tree, like 50, 100, or 200.
It's all about the math and unlike the clown two clicks to the north I don't profess to understand a great deal of it yet, to make it conform to any other product other than god damned options.
Anyway, you likely got the valuation idea from my request in the implied volatility thread so the links and information contained in it is a decent place to start.
And you might like this:
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