# Is Complete Vega Elimination Possible?

I avoid short selling in my strategies. Losing more than invested is not attractive. But at times the implied volatility is too high, I am worried about buying at all and I am trying to filter the effects of Vega so I can peacefully focus on my techniques without worrying about the fall of IV that brings down the option price.

Option A: Price 100 Vega: 5 Delta: .5

Option B Price: 10 Vega:1 Delta: .05

I thought Buying 1 lot of Option A and selling 5 lots of Option B would nullify the effect of Vega but leaving more delta in option A. But the trade gave some weird results(Option B lost more than A earned even when market moved in right direction). I know, I need to experiemnt it more. Before that, "Is Complete Vega elimination possible? Are there any popular techniques used?"

Thanks.

• Can you elaborate on 'option B lost more than A' do you mean in percentage or absolute terms? Can you give a small example? I quite not get your problem right now.
– Phun
Commented Feb 13, 2016 at 13:14
• volcube.com/resources/options-articles/… may or may not be helpful
– user59
Commented Feb 13, 2016 at 15:13

## 3 Answers

Constant Vega Requires Options Weighted Inversely Proportional to the Square of the Strike. E.g. if you have the following portfolio of options: $$\int_{S_i(t)}^{\infty}\frac{2\Big(1-\log[\frac{K}{S_i(t)}]\Big)}{K^2}C_i(t,\tau,K)dK+\int_{0}^{S_i(t)}\frac{2\Big(1-\log[\frac{K}{S_i(t)}]\Big)}{K^2}P_i(t,\tau,K)dK$$

You have a portfolio with a constant vega. You can find the proof on the appendix A of Demeterfi et al.

• Hi, I am going through your link. But before that, What mathematics I need to learn to understand these kind of formulas? What mathematics I need to master to become a Quant? Commented Feb 14, 2016 at 12:24
• That's a question that could deserve a topic in itself. You should know a bit of Stochastic Calculus ... Commented Feb 14, 2016 at 12:46

Well , complete elimination of even Delta is not possible, forget about Vega. When I say this , I'm talking about the trouble you'd face if you keep dynamically hedging your position from time to time. I mean it's not practical , however theoretically feasible it may seem.

But anyway if you're interested, below ways could be of your help.

1. You might want to utilize Vol-Indices ( VIX - CBOE and others ) and take appropriate exposure suiting your existing positions

2. You could reach out to fund houses and IBs to enter into client-taylored structured products like Vol/Var Swaps etc.. but that maybe a barrier as well in case you're a retail trader. You could have a very rough replicated structure as well for this - as mentioned by 'volcompt' but that may be tough to maintain dynamically.

Well there could be more ways to go about this, but that's all what I could think of.

Gud luck with that !

In general only non-linear instruments, like options, posses vega. Vega is always positive, no matter the directional component. So when you are long either a call or a put option you are long vega and when you are short either a call or a put option you are short vega.

Thereby it becomes clear that you can go long and short different option positions to offset vega. You cannot offset vega with linear instruments (underlying), i.e. stocks or indices (why? because their vega is zero!)

Two strategies come to mind: Risk-reversals and synthetics. A synthetic is a risk-reversal (simultaneous buying and selling of a call and a put) with the same strike which results in something similar to a futures contract. So basically by combining two non-linear instruments to replicate a linear one you eliminate vega.

See also this nice explanation: http://www.option-trading-guide.com/synthetics.html

Some general things to bear in mind:

1. The more sources of risk you hedge away the fewer potential revenue streams remain. When you hedge all greeks you will loose the spread of all those positions -> so turning this around, this makes sense only for market-makers (and even they don't hedge all greeks completely).
2. You still have to deal with model risk, e.g. when you use BS to calculate your hedges you will certainly be surprised by the outcome because of the non-normality of markets.
3. Most hedges only work dynamically, i.e. when the market moves, you have to re-adjust which can be quite costly.
4. Beware of ops-risk: You most certainly will not be able to establish all positions simultaneously with the limits you would like to have. Especially not in your example (high IV)!