# Aprox intraday implied volatility using intraday option prices and EOD greeks

I have two options datasets:

1. EOD IV and Greeks
2. Tick option and underlying prices

I'm looking to calculate IV for each tick. Is there a way to approximate the ticks' IV using last EOD Greeks and IV?

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no there is not (because the IV<->Price relationship is not linear, hence the name non-linear product), but there is an exact way to calculate your IV from the option tick prices and ticks of the underlying. Not sure, though, what benefit you would derive from doing that. –  Matt Wolf Jun 1 '13 at 3:36
@MattWolf Presumably there would be a performance benefit to approximating $IV_t$ from $\mbox{returns}_t$ and $IV_{t-1}$. Whether that would introduce too much error is application dependent. –  chrisaycock Jun 1 '13 at 12:35
@MattWolf I know there is no exact relationship, hence I'm asking for an approximation. As chrisaycock presumed, I'm looking for speed more than exactitude. –  Victor P Jun 1 '13 at 19:19
@chrisaycock, fair point made, yes of course one can approximate anything given there are past reference data that can be regressed. But as I said as long as you look to trade off such IV data approximations are not enough and introduce too much error due to the non linearity. If you can accept a reasonable estimation error then you can use the previous IV and underlying price relationship and derive the estimate of IV on the changed price of the underlying. But there is a reason why most all vol desks apply greeks in case they work off static IVs. –  Matt Wolf Jun 2 '13 at 2:17
Just to give you an example, if you only use IV(t-1) and OptionPrice(t-1) as well as OptionPrice(t) you may witness an unchanged option price from t-1 -> t and incorrectly deduce that IV must be about the same, while the price of the underlying moved down in the same observation period and IV exploded. Also, this is a very bad approach for short-dated options because you ignore delta decay as well as the effect of changes in vega with respect to the passage of time. –  Matt Wolf Jun 2 '13 at 2:30
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There are essentially two approaches you can take:

• Approximate changes in IV by establishing a relationship between IV and option prices through a function of IV solely dependent on option price. While it is computationally very convenient it introduces huge estimation errors in certain cases. As pointed out in my comment above one such case is a slide in underlying prices and accompanying IV shift up which you do not account for by only looking at changes in the option price. Also short-dated options will make your estimation almost worthless because you do not account for delta decay and changed in vega due to the passage of time (dVega/dTime) among other factors that affect short-dated options. I highly discourage you from taking the short route in case you deal with short-dated options. What you could do in this case is the following: Build in a filter and only run such approximation if

• you do not deal with short dated options
• fall back on a full-scale IV derivation if the underlying price return lies beyond a certain threshold
• Run a full-scale IV derivation by taking the last option and underlying prices and last observed IV and then apply all first-order greeks and for short-dated options some of the higher order greeks (I mentioned an example above). This will be computationally more intensive but it will be way more accurate.

As I mentioned I do not see much value in why you want to run an approximation in the first place. If you look to derive meaningful IVs then you need to run the full computation, especially if you look to extract IVs for further implied volatility model testing. If you look for enough accuracy to observe bid and offer implied volatility then you should not run any approximations at all. Also, if you have access to historical intraday greeks then I highly recommend to check with your data vendor, most likely they also supply past implied volatility data. Just my two cents.

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