If implied volatility changes, how much do I make or lose?
We can answer that question when we examine vega. Ironically, vega is not an actual Greek letter, so sometimes it is referred to as kappa. Vega is the measure of movement of an option’s price affected by implied volatility.
Before you learn how vega moves in accordance with time, strike price, and volatility, you need to understand what implied volatility is. Once we have put together the necessary pieces for vega, we will show you how this understanding can benefit you when trying to hedge a portfolio or a position.
Where To Find An Option’s Vega
Before we can even begin to define or talk about all the interesting attributes of vega, you need to know where to find the vega. An option’s vega, along with the other Greeks, come out of the option pricing model.
Due to the fact that Greeks are a byproduct of a calculation, means they have a model risk. A model risk means; the outputs are only as good as the inputs. If you plug in the incorrect implied volatility, you can’t expect to receive proper Greeks.
Model risk in terms of option pricing and Greeks is not a serious risk. Out of the 7 factors that affect an option’s price, only one of them is unknown: implied volatility. It would be difficult to mess up the model such that it throws off your Greeks.
It is more important to understand how Greeks are derived and that you can’t always trust the numbers for how they are.
The best place to find the vega of your option is through an option chain. An option chain displays all the calls and puts for a given expiration and underlying. You can usually customize your option chain to display the various Greeks in which you are interested. Most traders will use their option brokerage, but you can also use free tools such as Nasdaq.com to view an option chain.
What Is Option Vega
Implied volatility is always expressed as a percentage. Vega is always expressed as a dollar amount. A 1% increase in volatility will raise the option's price by the vega.
Let's develop this into an example. You have a long call on The Option Prophet (sym: TOP) with a premium of $5.50, vega of 0.20, and an implied volatility of 18%. If the implied volatility increases to 21% your long call is now worth $6.10.
5.50 (original price) + 0.20 (vega) x 3 (increase in volatility) = $6.10
When volatility begins to drop, it also drops our option premium. If our implied volatility goes from 21% down to 16%, our option will be worth $5.10.
6.10 (original price) – 0.20 (vega) x 5 (drop in volatility) = $5.10
Volatility is always expressed as a positive number for both puts and calls. A put's option price will increase as volatility increases in the same manner as a call’s price. As volatility goes up, option price goes up, as volatility goes down, option price goes down. Brian Overby notes, “Vega is positive when you buy options and negative when you sell them. The sign is not affected whether trading a call or put.”
What Is Implied Volatility?
Before we discuss how vega moves with strike price, time to expiration, and volatility, we need to better understand implied volatility. Implied volatility shows the "implied" movement in a stock's future volatility. Basically, it tells you how traders “think” the stock will move. Implied volatility is always expressed as a percentage; it is non-directional and is always displayed on an annual basis.
Currently TOP is trading for $50 and has an implied volatility of 20%. That means investors believe, in one year, TOP will be trading for $40 or $60.
50 (stock price) + 20% (implied volatility) x 50 (stock price) = $60
50 (stock price) - 20% (implied volatility) x 50 (stock price) = $40
The higher the implied volatility, the more investors think the stock's price will move. Stocks listed on the Dow Jones are value stocks, so a lot of movement is not expected; therefore, these stocks have a lower implied volatility. Growth stocks or small caps found on the Russell 2000, conversely, are expected to move around significantly, so they carry a higher implied volatility.
How Vega Changes Based On Strike Price
With options, everything is centered around an option finishing in-the-money. When options don't have a chance to expire in-the-money, they move very little and are not heavily affected by the Greeks. When an option is in-the-money, or at-the-money, the response to the Greeks is a lot stronger. This continues to remain true for volatility and vega.
Vega is the highest for at-the-money options. As we begin to move further away from at-the-money, towards out-of-the-money, and in-the-money, our vega begins to reduce. Deep out-of-the-money options have very little chance of moving in-the-money, so the weight of vega is very small.
How Vega Changes Based On Time To Expiration
The further we go out in time, the longer the expiration date, the higher vega will be. Why? The more days we have until expiration, the more time exsist for a move to happen, which means there is more uncertainty in the way the underlying will move.
As we move closer to expiration, we typically have a good idea of how the underlying will move. It is easier to call a one-day move versus a six month move, or even a month-long move for that matter. The closer we are to expiration the lower our vega is, and the smaller effect it has on our option's price.
How Vega Changes As Volatility Changes
Implied volatility also has an effect on vega. Implied volatility is the prediction of how an underlying will move in the future. As implied volatility increases, the strikes become closer to at-the-money. An example will help explain.
TOP is trading at $50 with an implied volatility of 10%, so traders think the price will end up at $45 or $55 (remember implied volatility is non-directional). The 40 strike put is 20% out of the money. Your vega on the 40 strike is probably low because the chance it will finish in-the-money is low. But wait! Implied volatility is now beginning to rise and has made it all the way to 25%. Now traders believe the stock will end up at $37.50 or $62.50. Suddenly your 40 strike put is not so out-of-the-money and has a good chance of finishing in-the-money, naturally our vega begins to increase.
How To Hedge Your Portfolio With Vega
Now that you have a firm understanding of vega, we can begin to construct your portfolio and hedge it with long puts. As the market, or stock, begins to move lower; your implied volatility will begin to rise. This is the natural negative correlation implied volatility and the underlying movement carry. Knowing this and what we know about vega, where would we set your hedge to expire? It wouldn't make sense to buy hedges that are short term. That would cost you a lot of money, and you know that vega decreases as we get closer to expiration. When looking for a hedge, we want to think further out. Perhaps we start looking six-months out because we know vega will be higher and our option price will move more as implied volatility begins to rise.
As for our strike selection, we can also make some assumptions. Even though at-the-money strikes have the greatest vega, you don't want to pick those for your hedge. First, they would be expensive, and you don't want your hedge killing your profits (that is opposite of what we are looking for), and second, you know that out-of-the-money options begin to act more like at-the-money options when implied volatility rises. Not only do out-of-the-money options respond better to higher volatility levels, but it can increase their premium substantially.
In the future, when you are looking to hedge a portfolio or a position, don't discount out-of-the-money options that have six-months to a year to expire. You will be surprised at how well they move when things are looking their worst.
Volatility is one of the greatest tools available to an option trader. Mastering and understanding all the nuances can be difficult and time consuming. The first thing you need to do is understand the basics of implied volatility and how they affect the overall option premium through vega.