Perhaps we wouldn't have needed Einstein and his Theory of Relativity if we'd been trading options earlier. We would have discovered much sooner how easy it is to bend time. All one has to do is to change the implied volatilities of the options in a position, and it's as if the time to expiration has been stretched out or shrunken.
Let's let author and CBOE instructor Jim Bittman teach us about this effect. First, however, we need a little discussion of mathematics with respect to options pricing. Theta describes how option prices change with the passage of time. For most quotes we see on the Greeks of a particular option, that unit of time is a day or a trading day. We could have a whole article devoted to whether that unit ought to be a calendar day or a trading day, but let's not be that technical. It doesn't matter that much for our purposes.
We options traders know that if the underlying's price was to remain the same straight through to expiration, that option's price is going to decay. All the extra or extrinsic value is going to leak out of in-the-money options. Out-of-the-money options are going to decay to zero since all their value is extrinsic. Therefore, theta is represented as a negative number for long options that we've purchased. This reflects the fact that value will be subtracted from the option as each day passes, barring other changes in the option's value. Here's where it gets tricky for those not accustomed to thinking about negative values. The more negative the theta, the lower it is, yet the higher its absolute value is. A theta of -15 is more negative, is lower than a theta of -7, yet its absolute value, 15, is higher. The more negative the theta, the more the option decays with the passage of time. The less negative the theta (the lower the absolute value), the less the option decays with the passage of time.
When we've sold an option, we have to multiply the theta by the number of contracts sold (a negative number), so we have to remember that converts the theta to a positive number, as in -(-15) = +15. Theta will be converted to a positive number for options we've sold. We've sold them at a certain price and we want their price to go lower so that we can either buy them back for less than the credit we received or else let them expire worthless in some cases, and keep all the credit.
Now we can get into Bittman's discussion of theta and volatility. Because of the way Bittman explains the concept, you'll soon see why we needed that prior discussion. On page 111 of Trading Options as a Professional, he writes that the "thetas of in-the-money, at-the-money, and out-of-the-money options decrease (increase in absolute value) as volatility increases." If we don't understand the mathematics, that sounds a whole lot like an increase in volatility helps out the long option holder because he uses the word "decrease" with respect to the theta. We now have reminded ourselves, however, that a decrease in a negative number means that it's getting more negative. Its absolute value is getting larger. The option's value will decay even faster. Usually, if we already own that option and volatility increases, that's going to plump up the value of the option, but what if we've unknowingly bought an option that had an unusually high volatility that had temporarily plumped up the value? How is it going to decay as time passes?
Perhaps you also know that option decay doesn't happen in a straight line. For options less than 30 days from expiration, that decay gets rapidly steeper as the time to expiration shortens, especially in the last week to ten days. When we think about Bittman's comment about how an increase in volatility impacts the option's theta, we can visualize what's happened this way: It's as if option's theta has been transported forward in time, when the time-related decay will accelerate as expiration draws closer. So, changes in volatility can make the option act as if expiration is closer or further away than it was before the volatility changed. Perhaps we're used to buying an option about three or four weeks out from expiration, for example, and we don't typically expect it to decay all much due to time-related changes if we hold it for a day or two, but if volatility had plumped up its value, we can expect that time-related decay to perhaps be more typical of what we would normally see a week closer in to expiration. Of course, many factors are coming together here to impact the pricing of an option, including other possible hikes in volatility if some news looms.
Volatility changes also act on the theta of complex positions, either slowing or speeding up time decay. Sometimes those in complex positions are entering theta-positive trades and they want decay. Sometimes, complex positions such as debit spreads are still theta-negative positions, and traders with those want less decay. When you're doing your end-of-the-day check of your positions, look at what a price change might do to your position, but also roll the volatilities up or down a bit, too, if your platform offers that possibility. Many do. You can also find freeware that will. Rolling the volatility in this way rolls it equally on each of the options comprising the position, and that's not exactly the way it works in real life. However, this test gives you at least a little better look at what might happen to your position as a result of any changes in volatility. If you've listened to former market maker Dan Sheridan's free seminars on CBOE or one of the brokerages, you've probably heard him make this recommendation, too. Our theoretical profit/loss charts or analysis pages don't always give us a perfect view of what will happen to our positions as a result of certain price or volatility changes, but they do give us an edge in looking forward in time. Take advantage of them.