No, dude... Think!! What is vega? What are the units of vega? If you divide vega by the change in IV, in what units is the resulting quantity going to be measured?
You're right, it's vega times IV change. So if IV goes up 2 pts accross the portfolio, the value will increase/decrease by 2*portfolio vega. So if I've lost $300 with a 3000 vega, IVs have decreased by 300/3000=0.1 pt accross the portfolio...or am I lost completely? However this assumes all the loss is from IV change, what about price movement and other greeks? Im still not fully understanding it
You know what the vol is before and what the vol is now. So pnl = delta pnl + gamma pnl + theta pnl + vega*(today ivol-yesterday ivol) + noise
Yes, this is the gist of it... However, a couple of points: 1) Firstly, if your portfolio contains a whole bunch of options on a variety of underlyings, there really is no such thing as "IV goes up 2 pts across the portfolio". What you need to do is perform the vega times change(IV) for every option in your portfolio to get vega PNL per line item and then sum up the individual vega PNLs to produce the total vega PNL for the entire portfolio. 2) You're confused about the point of this calculation. What we're talking about is the process of "PNL explain" or "PNL attribution". The idea here is that at any given time, when you observe that your portfolio PNL is X, you should be able to be able to attribute how much of the X comes from vega, how much from delta, etc etc. So the fact that X = $300 and that your total vega is 3000 doesn't at all mean that IVs have decreased by a particular amount across the portfolio. In fact, you shouldn't even be thinking across these lines. Idea is that some element of the $300 total comes from vega and the calculation in 1) above will be able to tell you what that is. You perform a similar calculation for delta, gamma, and whatever other factors you think are significant. You sum up the resulting factor PNLs and hopefully you get smth close to $300. Congratulations, you have just performed a PNL attribution exercise and can proceed to the next part, which is to try to explain/jawbone the residual. EDIT: cross post w/neww.
1) That makes sense indeed. IV change * vega per option and then sum up, gotcha. Only problem is vega varies, no? So if I have 50 IV and 2 vega for an option, it predicts a $2 increase in price if IV increases 1 pt. However if I calculate it after the fact, where vega may be say 3 or 4, I have a 1 IV change and 4 vega, which adds up to a 4$ increase in price (Whereast the real increase only was $2). Or maybe this isn't an issue, I dunno... 2) Yes I realized the calculation in my previous post was off, since it would attribute the entire PNL change to just vega alone. And yes I agree PNL attribution is what I'm looking for, didn't know it had it's own term. Then again thats what Im here for, to learn... Yes this makes sense. So to sum it up, vega is a result of vega*IV change. Which is obvious but I always overcomplicate things. Okay so now I need a way for Excel to snapshot the IV value which I will be comparing against in the future. I could use yesterdays IV ofc but I'm not sure if I have that data available.
Vega varies, indeed, but consider two things... 1) What you're doing here is producing an instantaneous PNL attribution, i.e. you're trying to explain your PNL at any given point in time, assuming that time freezes, so to speak, at that point. So a constant vega is not such a bad starting point. 2) However, you're correct. In theory, pretty much all greeks exhibit a degree of "convexity" (e.g. vega * change(IV) is poorly defined, because you actually have two vegas; think of convexity as the "vega" of the vega, dVega/dVol, vomma or whateva floats your boat) or sensitivity to other, supposedly independent factors. BTW, gamma is actually an example of convexity of delta. At any rate, in reality, unless you're running a massive book of options and/or are into exotics, you probably don't need to worry about these convexities and the various cross terms. A "fudge", such as using one of the vegas or an average of the two, is likely to be good enough for most peoples' needs.