How is the Long Call Affected by Volatility?

Do you understand how volatility effects the price of options? Do you know how the price of the underlying asset effects volatility? Do you understand what happens when they’re both moving? It gets a bit confusing. Hopefully, the following article will help you sort it all out.

This article, the first of two, will address the relationship between implied volatility (IV) and the movement of the underlying. Specifically, it will look at the positively correlated delta of a long call.

Very often it happens that an option trader purchases a long call that is in the money or at the money and the underlying goes in the correct direction, yet they still lose money on the call. Most of the time, this is due to the fact that the time has decayed, or the implied volatility has changed; or the possibility that there was a combination of both time decay and a change in implied volatility. However, to keep it simple, we will exclude theta, or time decay, from our discussion. In the next three figures, we will strictly place our focus on two dimensions of options: Movement of the underlying and IV change.

Underlying Movement IV Change Outcome Reference
+ c Up Up Double good 1a
+ c Down Up Bad * 1b
+ c Sideways Up Good * 1c
Figure 1

Each of the charts is arranged in the same way – displaying the facts. Only a long call is under scrutiny at present. Also, the reference numbers on the right are there to make a quick reference to specific scenarios. Starting with the 1a scenario; a long call is purchased and the underlying has moved up which is good. Simultaneously, the IV has also increased after the purchase of the option. The outcome for 1a is double good.

Next, let us suppose exactly the opposite scenario: The stock has gone down, and due to the drop in the market, fear has crept in so IV has exploded to the upside. Assuming that the underlying has plummeted, the IV increase did not help; hence, the conclusion for the 1b outcome is BAD. Disclaimer note: We are making a lot of sweeping generalizations here because many of the specifics are missing. So, for that reason, if there is a star next to the outcome result, this can be interpreted as “Depends on the Specifics.”

In the case of 1c, a long call is purchased due to the belief that the underlying is going to take off, yet instead, it is just chopping around in sideways motion. For every passing day, during which the stock goes sideways, there is time decay, so this is not good. On a positive note let us assume IV has increased significantly. In this case, “significantly,” meaning the IV has increased more than the theta has decreased. In other words, not only did the IV change neutralize the time decay, but has also added a bit of value to the option premium. The end result is good, although the underlying has gone nowhere direction-wise. The IV has helped to maintain the value of the premium, and increased it a bit. Be aware that there could many variations within the 1c scenario.

Underlying Movement IV Change Outcome Reference
+ c Up Same Good * 2a
+ c Down Same Bad 2b
+ c Sideways Same Bad 2c
Figure 2

Figure 2 still has the three possible directions that the underlying could go, but the assumption is made that IV does not change. In reality, the scenarios in Figure 2 are not possible because IV is a living thing and it is constantly changing. However, if IV were to freeze by some anomaly, the outcomes are as listed above. The 2a outcome for the stock going up and IV staying the same depends on how much the stock has gone up because there is still time decay that needs to be overcome. The bottom line for the 2b and 2c scenarios is that they are both bad. Again, do not spend too much time entertaining the possibilities from Figure 2 because they are not likely to happen.

Underlying Movement IV Change Outcome Reference
+ c Up Down Depends 3a
+ c Down Down Double Bad 3b
+ c Sideways Down Bad 3c
Figure 3

Figure 3 shows a decrease in the IV, so that in the 3a scenario, the stock has gone up and IV has dropped. The outcome truly depends on how much the underlying has gone up and exactly how much the IV has dropped. Therefore, rather than making blind statements, we’ll just state the outcome as – Depends.

In the 3b scenario, the underlying has gone down as well as IV, which is not necessarily possible, but assuming it happened, the outcome would be double bad. The purchased premium has lost its intrinsic value due to the drop in the underlying as well as the IV drop.

The 3c outcome is also bad because the long call did not increase in value; there was not a lift in the stock, and the IV has decreased.

In conclusion, most of the time when the broad market goes up, the implied volatility decreases to an extent, depending on various factors. The specifics of how much IV has dropped, or how far up the market has moved, and over how many days, has been left out of the equation because we are attempting to make some generalizations for your learning. When the underlying is up, then IV is usually down. On the other hand, most of the time when the broad market is down, that very same day, the VIX and IV tend to go up. The underlying is down, but the IV is up. The only norms within all the different scenarios discussed above are: 1b in the first Figure for a down market, and 3a in Figure 3 for an up market. This draws the question: Is a plain long call the best that an option trader can come up with? Connect the dots yourselves.

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