Hi guys, First time posting here. Pleasure to join the forum. I'm in the process of calculating the historical implied volatility of every single option traded over the last ten years using end of day historical prices. Sometimes, I run into situations where an arbitrage has occured, for example a call option that strikes at $10, spot's at $13, but the bid, ask, and/or last price of the option is something like $2.95, leaving a $.05 arbitrage. So when I plug this data into my blackscholes function, the blsimpv() in Matlab, I get a big fat 'NaN', saying the function cannot compute. I approached this by factoring in the transaction costs that market firms would naturally incur to the bid/ask/last prices for my black scholes equation. However, arbitrage conditions still pop up in my dataset. Has anyone dealt with an issue similar to this before? How would you deal with the implied volatility of an option trading at an arbitrage? Cheers,Ben

There will be lots of this for various reasons -- just drop them

what sort of options ? American style on single stocks ? Or European options on indices ?

Hello,As Alan said there are loads of reasons for that.As daveangel said if you are dealing with American Options, do you take into accounts dividend and what rate are you using for financing your position, is the exchange making people to pay the premium up-front, what kind of margins is it required to finance your position...I would add more specific ideas for you to be convinced:If you are using the last price of the options, then it means than the last time the options traded it was at 2.95$, but do you know exactly when it traded, do you have the exact tick data ? If you have 1sec data maybe during this sec the market move and the options didnt trade another time so you see a last which hasnt moved while the market moved.Or maybe that at the time it traded the bid/ask of the future was wide, you saying 13$, is it a Mid ?Imagine the options is ITM, so have great delta and the future price moved quickly but the market-maker didnt had the time to update his options quote before being lifted/hit, it traded as an apparent arbitrage, assuming the other guy successfully hedged his options quickly after and still you shall take into consideration the fees of the hedge.You can also have error or mistiming in your data and There really are loads of other reasons for that to happen.ex: Im on an illiquid stock(stock is illiquid or become temporary illiquid because of some Corporate Action for example), a broker cross a 10$ call at 2.95$ when the market is at $13, in fact my broker did the hedge lower and he didnt crossed it before the market rose so it traded as an apparent arbitrage while it was not, there is no way for you to know this.Dont try to have double digit precision on vol for this, it makes no sense. Honestly , for a big historical knowing it traded 23% or 23.5% is already really good, if you wanted to build a short term trading model you wouldn't use 10 years historical anyway.Good luck.

Thanks for the replies, that's great information. In light of what Jige has said, I have decided to drop the 'abritraged' data as Alan has suggested.I simply do not have the time to figure out what went wrong for that much data. And as you said Jige, little marginal utility to be gained for my purposes in doing so anyways. Yah, they were american options. Thanks for the help guys. Glad to have joined this forum.