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.