Serving the Quantitative Finance Community

 
User avatar
Skywalker
Topic Author
Posts: 1
Joined: April 7th, 2003, 9:43 pm

Best way to average option prices?

November 9th, 2007, 10:59 am

I am trying to calculate a single value that represents all available options for a specified underlying (i.e. across all strikes and maturities). A number of methodologies spring to mind, but I would like to hear from the more experienced, as to the best way to do this.Thanks
 
User avatar
PaperCut
Posts: 0
Joined: May 14th, 2004, 6:45 pm

Best way to average option prices?

November 10th, 2007, 9:20 pm

At first blush, this is insane. Mind you, I've had plenty of insane thoughts myself, so I guess I can't say that insanity is really unusual or bad. Just don't do anything "financial!"Seriously, what are you trying to do?If you are trying to find a quick and easy metric that points toward option values/valuation, think about it: this is what Black-Scholes volatility is supposed to do! However, it was found that this is inadequate for the full complement of option prices; in other words, we need many vols to describe all these option prices - hence, vol loses its "explanatory" power and becomes just some sort of index, relevant for each option, one at a time. Ok, now introduce the next idea: how about stochastic volatility / Heston. Now we have a new set of parameters; inst. variance, long variance, speed of mean reversion, level of mean reversion, vol of vol...however, guess what? You'll find this model does a pretty poor job of describing all of the option prices you mentioned. So, how about Heston with Jumps? Hmm, this works really well, but now there are more parameters...Savvy?
 
User avatar
Skywalker
Topic Author
Posts: 1
Joined: April 7th, 2003, 9:43 pm

Best way to average option prices?

November 12th, 2007, 9:46 am

Thanks for your feedback 'PaperCut'Actually, what I'm trying to do is not quite as 'outlandish' as it may seem at first. i am simply trying to work out an averaging methodology so I can create indices (this is similar to the volatility index calculated by the CBOE and other exchanges) - but the difference here is that I want to use premiums rather than implied volatilities - hope that helps clarify what I'm trying to do.
 
User avatar
amit7ul
Posts: 0
Joined: December 7th, 2004, 8:36 am

Best way to average option prices?

November 12th, 2007, 12:07 pm

i am totally ignorant as far as this index making technology goes, but i thinkinterest rates are an index and they are inputs(some kind of mean level) to defining possible distributions of interest rates at future horizonsvolatility index is again some indicator and an input to define a distribution of returns, so i think, i see a pattern in terms of moments of distribution. the average option price you are talking doesn't give any intuitive feel about location/scale etc of distribution.
 
User avatar
Skywalker
Topic Author
Posts: 1
Joined: April 7th, 2003, 9:43 pm

Best way to average option prices?

November 12th, 2007, 2:11 pm

Perhaps a more clarified (i.e. 'well formed' version of the question I am asking is this) - Concentrating on a single maturity (for simplicity) :1). How may I adjust calculate a single WEIGHTED average price of options for all strikes of options with the same maturity?Hint: The weighting scheme must factor in the observed skew (i.e. smile/grimace across the strikes for the selected maturity month).
 
User avatar
merx
Posts: 0
Joined: October 18th, 2007, 5:06 pm

Best way to average option prices?

November 13th, 2007, 2:53 am

Option data are usually a bit tricky to deal with. In what you are trying to do I think you may run into a couple of issues:1. Option quotes for many of the strikes are very old. So you can't use all the strikes, you'll have to look and see if there was a trade recently. 2. Depending on your weighting scheme, the bid/ask in quite OTM options may be a problem. There are a few other issues to deal with that I can't remember at the moment - scan the academic reseach pertaining to options in the market microstructure literature. Otherwise, good luck!
 
User avatar
PaperCut
Posts: 0
Joined: May 14th, 2004, 6:45 pm

Best way to average option prices?

November 13th, 2007, 3:49 am

I tried.
 
User avatar
Skywalker
Topic Author
Posts: 1
Joined: April 7th, 2003, 9:43 pm

Best way to average option prices?

November 13th, 2007, 6:57 am

Thanks Merx (et al), I think I know how to proceed now.