# What does it mean to be “long or short in volatility”?

I've heard a question regarding pricing of european calls. The question is:

Is the call long or short in volatility when it is (deep) OTM? What is the profile of the implied volatility?

I know that in that case the answer is "long". Conversely the call would be short in vol if it was ITM.

I see a relation between long and the wish that volatility is high in order to go ITM if you hold the call. Also if you are ITM, I can see that your interest is to continue ATM. Therefore you want the volatility to be low.

I don't understand what exactly this term means neither where it comes from. I guess it is related to volatility trading/arbitrage.

Could someone please help me out and give me a precise definition for the term "long/short in volatility"?

I'll expand on Mark's and SRKX's answers which are both correct but brief. To be clear the words long and short have been generalized in finance. They used to mean that you owned a stock or had sold a stock short. Now they are often used to say you make money when a value goes up (long) or make money when some value goes down (short).

In this case whenever you own a call or a put you are "long" volatility. Meaning that as volatility increases the value of your position increases (holding everything else the same). How much added value that you get for a certain increase in volatility (called vega) depends on how in/out of the money the option is at currently among other things, but if you own the call/put it is always positive as more volatility means more possible upside.

When you sell calls or puts, then volatility decreases are good for your position so you are called "short" vol.

• I do not agree. If the stockprice is close to zero, the put has its maximum value. Hence any additional volatility can only reduce value i.e. negative vega. – emcor Jan 22 '15 at 23:47
• @emcor negative vega? I don't think that's possible, is it? I mean, the whole idea is that you can replicate an option payoff by holding a portion of the stock and that portion of the stock is determined among other things by volatility I understand. The more volatility the more of the Stock you need to hold and the more the option is worth then right? – SRKX Jan 23 '15 at 7:13
• put-call parity guarantees that a put and call with the same strike have the same vega. a very OTM call definitely has positive vega – Mark Joshi Jan 23 '15 at 20:38
• @emcor interesting example, though I think you would have trouble trading on it. However, theoretically (infinitesimally small moves) you are not correct as though it is near its maximum value it is not quite there. The vega would be nearly zero but still positive. – rhaskett Jan 26 '15 at 20:05
• The concept of vega breaks down at this point. Remember vega is the change in the value for a small change in the volatility of an option holding all else (including the price of the underlying) fixed. As the price is "fixed" it being close to zero doesn't really matter. In your extreme case, none of the greeks really apply and even measuring volatility would be funny as well. At this point, people often use state models looking at the probability of various futures like bankruptcy and the option payoff in those cases. – rhaskett Jan 26 '15 at 20:28

the vega of a call is always positive. The holder of a call option is therefore long volatility whatever the spot price.

Mark Joshi's answer is absolutely right, but just to elaborate a bit:

The Vega of an option is the sensitivity of its value with respect to volatility $\nu = \frac{\partial V}{\partial \sigma}$.

For calls, it makes sense that the Vega is always positive, not matter the level of the underlying.

If you take the Black-Sholes model, you can find the theoretical value of Vega here.

• Thank you for your answer.I am OK with that. Could you develop a bit and answer the questions please? Why the terms "long/short" and when do you employ each of them? Also by your's and Joshi's answers a call is always long in vol no matters its moneyness or I misunderstood it? – Cooper Jan 22 '15 at 12:31
• "it makes sense that the Vega is always positive" how does that work?^^ – emcor Jan 22 '15 at 23:44