confused about vega

lezebulon · 7/1/14

Hi
sorry this may be the wrong board
recently I've been thinking more about implied vol surface, and now the notion of vega doesn't make any sense to me
I have 2 questions that are somewhat related:

1) when talking about a product made of several options, for instance a strangle, what is the real meaning of being long vega ? Obviously the implied vol is different for each contract that makes the strangle, so what does it mean mathematically ?
2) more generally, what is the point of measuring the vega on real option data ? For instance, let's say a call of a given maturity and strike has an implied vol of 20% , it's possible to compute its vega. Now, let's say that the next day, the underlying didnt move (and I ignore the value lost by theta either), yet the option price increased. We will compute the new implied vol and conclude it increased. In that case, we will say that the change in pnl is due only to vega-pnl, but for me it has no meaning at all since the change in implied vol is made-up by the option prices, and doesnt explain anything more than just knowing that the option price increased.

Can you help me on this ? Thanks!

CasanovaJ · 7/1/14

1) A long position in an option (regardless of whether a call or put) increases in value with increased expectations of vol-- the expected upside is higher, and the downside is still limited to the amount of the premium. A strangle is just a position in a long call and a long put on the same underlying (so both components of the strategy are long vol), so the long position in the straddle is long vol.
2) Ignoring theta (and rho too for that matter) if the underlying doesn't change in price but the price of the option increases, it's because people's expectations of the underlying's future vol have increased, which shows up mathematically in the higher implied vol calc.

lezebulon · 7/2/14

Hi
sorry I wasn't very clear:
1) I took a bad example to make my point. Now instead of a strangle, imagine I have +1 call of a given strike, expiry and -1 call at a bigger strike, same expiry. How is the vega defined in that case, since there are two implied vols that can move separatly (one for each call) ?
2) I know this, what I don't understand is why is the vega-pnl relevant at all. Assume there is no move in the underlying, interest rate, and we ignore the theta. If from one day to the next, the price changed by 0.1, we can attribute this to vega-pnl (which will be somewhat off anyway), but what is the actual point of doing that ? How is it better than just saying "this change in pnl is due to a change in implied vol" , or "the remaining factors that determine the price changed", since it's basically all we know ?

CasanovaJ · 7/2/14

1) If the two calls are on the same underlying and have the same expiry, the vega is additive... the long call will have positive vega, the short will have negative, add them together, and the result is the overall vega--
http://www.volcube.com/resources/options-articles/vega-neutral-trading-strategies/
2) If you have predictions for future vol, it can be interesting calculate the impact that it will have on the option you're looking at... yes if you see the price going up when the underlying hasn't moved you know that it was (largely) because of changes to implied vol, but how much did it move based on how much of a change in implied vol, and if you think vol is going to go up by x, how much could you expect to make by buying the option?

lezebulon · 7/2/14

CasanovaJ said:
1) If the two calls are on the same underlying and have the same expiry, the vega is additive... the long call will have positive vega, the short will have negative, add them together, and the result is the overall vega--
http://www.volcube.com/resources/options-articles/vega-neutral-trading-strategies/

sorry but why would the vega be additive in that case ? aren't you and your link completely disregarding the skew ? from one day to the next, the i.v of the long call can go up, and the i.v of the short call can go down; in that case how was the total vega useful ?

For 2) I understand a bit more. However, why would a foresight in i.v change be more meaninful than a foresight in the change in option price ? Since we are not talking about predicting that the vol of the underlying will go up, but predicting that the i.v of a given call will go up ? To me the second one doesn't have a lot of meaning in the "real" econominal world

C S · 7/2/14

lezebulon said:
sorry but why would the vega be additive in that case ? aren't you and your link completely disregarding the skew ? from one day to the next, the i.v of the long call can go up, and the i.v of the short call can go down; in that case how was the total vega useful ?

For 2) I understand a bit more. However, why would a foresight in i.v change be more meaninful than a foresight in the change in option price ? Since we are not talking about predicting that the vol of the underlying will go up, but predicting that the i.v of a given call will go up ? To me the second one doesn't have a lot of meaning in the "real" econominal world

1) vega is price sensitivity to change in the underlying's volatility. More precisely it's the derivative with respect to vol. and the derivative is additive (even linear).

2) that's funny. I'd say the "vol of the underlying" has less meaning in the "real world". You can ask two people to compute the vol of a stock and you'd be lucky to get the same answer. Whereas the implied vol of a call option is well defined. Basically the price is the implied vol and it reflects, in the very liquid options markets, the expectations of all market participants. So it has a real economic meaning, like the VIX.

lezebulon · 7/3/14

C S said:
1) vega is price sensitivity to change in the underlying's volatility. More precisely it's the derivative with respect to vol. and the derivative is additive (even linear).

vega is the sensitivity to *implied* vol of the option, so there's no reason that for 2 different options, the implied vol will move by the same amount during one day, so what's the point of summing them?

CasanovaJ · 7/3/14

lezebulon said:
vega is the sensitivity to *implied* vol of the option

"Implied vol" refers to the vol of the underlying, not the option

lezebulon · 7/3/14

I meant, vega is the sensitivity to the implied vol of the underlying, for the given strike, expiry of the option. Am I right saying that if you have 2 options, there is no reason that the implied vol of both options will increase by the same amount in one day? In that case, you have a vega for option 1, and vega for option 2, and there is no logic in summing those

CasanovaJ · 7/3/14

lezebulon said:
Am I right saying that if you have 2 options, there is no reason that the implied vol of both options will increase by the same amount in one day?

The vol is of the underlying, and vol of the underlying doesn't change based on the characteristics of the options on it. It's the same underlying, vega is a partial derivative, and partial derivatives (with respect to the same independent variable) are additive.

lezebulon · 7/3/14

I don't get it... I'm talking about seeing in the market 2 options, with different strikes, and different prices.
How do you define/compute the vega for each option in that case, if you are now talking about the vol of the underlying share (how is it even computed with real option data ? ). As far as I know if you use the vol of the underlying to price the options, you won't match the market price for both options because of the skew, which is why we use implied vol. In that case, you have one implied vol for each option and you can define the derivative of the price wrt its implied vol

CasanovaJ · 7/3/14

If you start thinking in terms of vol skew, you'll need to start looking at the correlations between the implied vols... the vega is only strictly additive if you ignore skew and assume the implied vol of the underlying will be the same for both options. The existence of skew, though, is not "the reason for using implied vol"... Implied vol is used because we're talking about a future number that's not observable and that (without a crystal ball) cannot be conclusively determined-- all we can do is back out assumptions of it based on current prices and a model that most people acknowledge is at least a bit flawed.

lezebulon · 7/3/14

CasanovaJ said:
the vega is only strictly additive if you ignore skew and assume the implied vol of the underlying will be the same for both options

sure, and I agree with you if you model the whole diffusion process with a normal B&S model, single constant vol for the price process.
However, on real option data (ie, the prices I observe today in the market), why would I ever ignore skew ? the implied vol is easily computable and will give me different values for different options, so each option's vega will actually refer to sensitivity to different implied vol points on the vol surface, which have no reason to move by the same amount

CasanovaJ · 7/3/14

lezebulon said:
sure, and I agree with you if you model the whole diffusion process with a normal B&S model, single constant vol for the price process.
However, on real option data (ie, the prices I observe today in the market), why would I ever ignore skew ? the implied vol is easily computable and will give me different values for different options, so each option's vega will actually refer to sensitivity to different implied vol points on the vol surface, which have no reason to move by the same amount

Yes I agree, but vega is defined as the "change in value based on a change in vol," and if you're looking for the "total vega of a portfolio of the two options" but you assume that there's skew, then which "vol" would you be trying to derive the total vega off of? Either you assume that there's no skew (in which case you can just add up the individual vegas), or you have to get extremely creative with it (which is why there are entire MFE courses and a ton of research dedicated to this).

lezebulon · 7/3/14

that's exactly the question #1 I was asking here :p
In many books / in practice, I read / hear about the vega of a strangle (for instance)... does it mean that, everytime, they simply ignore the skew ? In that case, is there any practical explanation for this HUGE assumption, other than convenience: ie, do we know that most of the time in practise the implied vol surface will only move in parallel from one day to the next ?

CasanovaJ · 7/3/14

OK, well, circling back to your original question then, personally my answer would be: "being long vega means that if you assume that there's no skew and that all the options are on the same underlying that has the same vol, then if the vol of this underlying increases, your portfolio will increase in value... if you assume that there's a skew, though, then you need to figure out how to model a volatility smile, which it seems like no one has really managed to do yet, at least in any 'established, industry-standard' way"... "how to model things in a way that will no longer assume normality" hasn't exactly been settled yet, at least to my (just-starting-his-MFE-in-September) level of knowledge...

lezebulon · 7/3/14

alright I get it, thanks for the explanation. I admit that I'm a bit shocked that summing the total vega is widely used, when at the same time the skew is also widely used, and that I see nowhere the mention that these 2 are incomptatible (or least, I never see the mention that a no-skew assumption is made when summing the vegas)

CasanovaJ · 7/3/14

To be completely honest, I am not an authority on this and am hoping that someone who has taken a course like this can add something--

http://ieor.columbia.edu/introduction-implied-volatility-smile

I can tell you, though, that yes, summing vegas is commonly done... I don't pretend to know all the background yet (which is why I'm beginning an MFE in a couple months), but I work for a large investment manager, and for derivatives risk management they do just use simple sums of all the Greeks (including vega)... I'm sure they know about the existence of skew, but in terms of what to do about it, I'm pretty sure that the answer for most people is still "who the hell knows"

C S · 7/3/14

Just to interject before heading for the hills this weekend..

If you want to take the derivative with respect to a curve, surface, element of a parametrized space of geometric objects, you have to develop a decent amount of differential geometry, even if you are being a physicist type and don't care so much about rigor. But it's possible. I wouldn't know what it gives you over the standard BS theory though.

financeguy · 7/5/14

I'm an options trader. Here's what we do. We look at the sum of vega (technically smile vega, not B-S vega, but assume B-S vega for these purposes) of all our options. We generally bucket by tenor, like 1M, 3M, 6M, 1Y, etc, as each point in the term structure doesn't always move in parallel. But again, we're talking about vol vs skew risk so let's just assume the curve does move in parallel for this exercise. Then when the implied vol of the ATM's go up or down, we expect our pnl from that happening to be our portfolio's vega times the move in the implied vol of the at-the-moneys. Now we also have sensitivity to how the smile moves. For that we have greeks defined as sensitivities to generic risk reversals and butterflies traded in the market, different places call them different things. So if, in addition to the implied vols of ATM options causing vega pnl we have the implied vols of risk reversals and butterflies moving, that will cause additional pnl for the out-of-the-money options in our book. We generally mark to generic % OTM risk reversal / fly or % delta risk reversal / fly, and then re-interpolate our smile and find what our change in implied vols were to each option in our book. In any case, any OTM option will have some vega, some sensitivity to risk reversal, and some sensitivity to butterfly prices. Then our expected pnl is the sum product of the three risks times changes in each smile parameter (atm vol, risk reversal, butterfly).

Also, generally speaking, vega is a good first order approximation of your risk, because if the ATM options go up in vol, it's very unlikely that the vols of any OTM options vols go down (and vice versa). So it's not totally silly to try to manage the sum of your portfolio's vega.

Hope that helps.