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Volatility and Time: Factors Affecting Option Premium

It is essential that people can make informed decisions about the opportunities derivatives present as well as the potential pitfalls. Volatility and time are two important factors affecting option premium that stand out in evaluating the central question of value.

Volatility and Time

It is common in finance for the core essence of an idea to be hidden behind complex language and the liberal use of mathematics. One of the objectives of the derivatives section of the Financial Pipeline is to make the revolution in financial engineering accessible to everyone so that people can make informed decisions about the opportunities derivative instruments present as well as the pitfalls they create.

In evaluating volatility, one question a derivatives professional might ask themselves when examining a particular opportunity is:
“If I buy this structure, will I be able to make more money trading the underlying cash instrument than I will pay in time decay over the life of the instrument?”

Conversely, the derivatives trader could have asked: “If I sell this product, will the losses I sustain trading the underlying cash instrument against this structure be less than the premium I am paid at inception?”

Let us restrict ourselves to the question facing the prospective buyer of this non-linear instrument. Think of it as a call option on a particular stock, for example “Dollar.com.” For the purpose of argument, assume that the current stock price is $100, our option’s notional amount is 100 shares, the option matures in three months and the strike price is $100.

Understanding Volatility

Volatility and Time

In evaluating this central question of value, there are two important factors affecting option premium that stand out: volatility and time. We will consider them both individually.

The higher the implied volatile-level of this product, the higher the premium will be and the more difficult it will be to pay for the option. However, if we expect actual volatility to be higher than the implied level, it may pay for us to own this option and to trade GE stock against it.
The key here is our expectation of what volatility will actually turn out to be as it relates to the implied amount.

For example, if the implied level on our Dollar.com call is 15% (on an annualized basis) in the marketplace, but we think that the actual level will be closer to 25%, we should buy the option. We will make more money delta-hedging the option (or rebalancing it in response to market movements) than we will pay in premium.

Now, what does it mean if implied volatility for our option in the marketplace jumped from 15% to 25% immediately after we bought our option? This might happen if there was an unexpected announcement from a takeover company, “Savage LBO LLC,” that they were going to make an unfriendly bid for Dollar.com. The outcome is uncertain.

Outcomes

First, for the option we own, we will see the premium jump higher since we will own something that has now increased substantially in value. Because the option is at-the-money spot (i.e. its strike is equal to the current spot rate), this effect is at a maximum. Recall that the change in the option’s value due to a change in implied volatility, all other things being equal, is referred to as its “vega.”

Second, we can see that the 3-month call we bought at an implied volatility of 15% is now worth what a 6-month call is worth, with the same strike before volatilities shot up in response to the announcement. Therefore, the higher move in implied volatilities is like an extension of our 3-month option into a 6-month option. It is as if we got three months for free.

Relationship Between Time and Volatility

Time value is the measure of how much money we should make if the stock turns out to be as volatile as the implied volatility says it should. Changes in the implied level of volatility necessarily mean changes in time value (and therefore premiums). We could make the same absolute amount of money delta hedging a short-dated option on a very volatile underlying as we could on a long-dated option on a calm underlying.

Article by Chand Sooran, Point Frederick Capital Management, LLC

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