Effects of Volatility on the Time Spread

When purchasing a time spread, the investor should pay attention to not only the movement of the stock price, but also the movement of volatility. It plays a very large roll in the price of a time spread, which is an excellent way to take advantage of anticipated volatility movements in a hedged fashion.

Option Volatility

Since the time spread is composed of two options, the investor should understand the role of volatility in options as well as in time spreads. Let us start with option volatility.

We measure an option's volatility component by a term called Vega. Vega, one of the components of the pricing model, measures how much an option's price will change with a one-point (or tick) change in implied volatility. Based on present data, the pricing model assigns the Vega for each option at different strikes, different months and different prices of the stock.

Vega is always given in dollars per one tick volatility change. If an option is worth $1.00 at a 35 implied volatility and it has a .05 Vega, then the option will be worth $1.05 if implied volatility were to increase to 36 (up one tick) and $.95 if the implied volatility were to decrease to 34 (down one tick).

Keep these facts in mind as we continue to discuss Vega:

1. Vega measures how much an option price will change as volatility changes.
2. Vega increases as you look at future months and decreases as you approach expiration.
3. Vega is highest in the at-the-money options.
4. Vega is a strike-based number. It applies whether the strike is a call or a put.
5. Vega increases as volatility increases and decreases as volatility decreases.

It is important to note that an option's volatility sensitivity increases with more time to expiration. Further out-month options have higher Vegas than the Vegas of the near term options. The further out you go over time, the higher the Vegas become. Although increasing, they do not progress in a linear manner. When you check the same strike price out over future months you will notice that Vega values increase as you move out over future months.

The at-the-money strike in any month will have the highest Vega. As you move away from the at-the-money strike in either direction, the Vega values decrease and continue to decrease the further away you get from the at-the-money strike. Remember, Vega (an option's volatility component value) is highest in at-the-money, out-month options. Vega decreases the closer you get to expiration and the further away you move from the at-the-money strike.

The chart below shows Vega values for QCOM options. Observe the important elements. The stock price is constant at 68.5. Volatility is constant at 40. Time progresses from June to January. Finally, the strike price changes from 50 through 80. Notice the increasing pattern as you go out over time and how the value decreases as you move away from the at-the-money strike.

Chart 3- VegaStock Price 68.5 Vol. 40
Strike June July October January
50 0 .008 .064 .114
55 .004 .030 .102 .153
60 .023 .063 .135 .184
65 .053 .090 .157 .205
70 .056 .094 .165 .215
75 .032 .077 .154 .213
80 .011 .052 .142 .203

Another important fact about Vega is that it is a strike-based number. This means that the Vega number does not differentiate between put and call. Vega tells the volatility sensitivity of the strike regardless of whether you are looking at puts or calls. Therefore, the Vega number of a call and its corresponding put are identical.

The chart below shows the Vega values for calls and the corresponding puts. As you can see, these values match up in every instance.

Chart 6
Strike Price Call Vega Put Vega
June
60 .023 .023
65 .053 .053
70 .056 .056
July
60 .063 .063
65 .090 .090
70 .094 .094
October
60 .135 .135
65 .157 .157
70 .165 .165
January
60 .184 .184
65 .205 .205
70 .215 .215

Vega can also calculate how much a specific option's price will change with a movement in implied volatility. You simply count how many volatility ticks implied volatility has moved. Multiply that number times the Vega and either add it (if volatility increased) to the option's present value or subtract it (if volatility decreased) from the option's present value to obtain the option's new value under the new volatility assumption. The calculation works on individual options and can analyze the value of the time spread.

Apply Vega to Time Spreads
Now, let us apply the concepts of Vega to the Time Spread. When you apply the Vega concept to time spreads, you observe that as implied volatility increases, the value of the time spread increases. This is because the out-month option, with the higher Vega will increase more than the closer month option with the lower Vega. That widens or increases the spread.

The chart below shows a time spread and its reaction to increasing volatility. Each time that implied volatility increases, the value of the time spreads increase. This increase would naturally favor the buyer.

Chart 4
Stock Price $ Vol. June/July 65 Oct/July 65
65.5 30 1.09 2.09
65.5 40 1.43 2.75
65.5 50 1.77 3.41
65.5 60 2.11 4.05
65.5 70 2.49 4.60

If an investor bought the time spread at low volatility and within a few weeks volatility had increased and pushed the spread price higher, the investor could sell the spread at a profit even before expiration.

Of course, the Vega can also demonstrate the opposing effect. As implied volatility decreases, the spread tightens or decreases in value. As volatility comes down, the out-month option with its higher Vega will lose value more quickly than will the nearer month option with its lower Vega. In the chart below, you will see how decreasing volatility affects the time spread's value.

Chart 5
Stock Price $ Vol. June/July 65 Oct/July 65
65.5 70 2.49 4.60
65.5 60 2.11 4.05
65.5 50 1.77 3.41
65.5 40 1.43 2.75
65.5 30 1.09 2.09

Glance back to Charts 4 and 5. Take note that the stock price is constant. The changes in the price of the spreads are due to the change in volatility.

We discussed how to use Vega to calculate an option's price when volatility changes. The same calculation method works for time spreads but the calculation is slightly more difficult.

Base Volatility

Spread traders must understand how to properly calculate accurate volatility. In order to get accurate volatility levels, you must first determine a base volatility for the two options involved in the spread. Getting a base volatility must be done because different volatilities in different months cannot and do not get weighted evenly mathematically.

Since they are weighted differently, you cannot simply take the average of the two months and call that the volatility of the spread. It is more complicated than that.

The problem relates to calculating the spread's volatility with two options in different months. Those different months are usually trading at different implied volatility assumptions. You cannot compare apples with oranges nor can you compare two options with different volatility assumptions.

It is important to know how to calculate the actual and accurate volatility of the spread because the current volatility level of the spread is one of the best ways to determine whether the spread is expensive or cheap in relation to the average volatility of the stock.

There are several ways to calculate the average volatility of a stock. There are also ways to determine the average difference between the volatility levels for each given expiration month. Volatility cones and volatility tilts are very useful tools that aid in determining the mean, mode and standard deviations of a stock's implied volatility levels and the relationship between them.

The present volatility level of the spread is comparable to those average values and a determination can then be made as to the worthiness of the spread. If you now determine that the spread is trading at a high volatility, you can sell it. If it is trading at a low volatility, you can buy it. You must know the current trading volatility of the spread first.

To accurately calculate volatility levels for pricing and evaluating a time spread, the key is to get both months on an equal footing. You need to have a base volatility that you can apply to both months. For instance, say you are looking at the June / August 70 call spread. June's implied volatility is presently at 40 while August's implied volatility is at 36. You cannot calculate the spread's volatility using these two months as they are. You must either bring June's implied volatility down to 36 or bring August's implied volatility up to 40. You may wonder how you can do this.

You have the tools right in front of you. Use the June Vega to decrease the June option's value to represent 36 volatility or use August's Vega to increase the August option's value to represent 40 volatility. Both ways work so it does not matter which way you choose.

We will use some real numbers so that we may work through an example together. Let's say the June 70 calls are trading for $2.00 and have a .05 Vega at 40 volatility. The August 70 calls are trading for $3.00 and have a .08 Vega at 36 volatility, so the Aug/June 70 call spread will be worth $1.00. To be able to calculate the volatility of the spread, we must equalize the volatilities of the individual options.

First, let's move the June calls by moving June's implied volatility down from 40 to 36, a decrease of four volatility ticks. Four volatility ticks multiplied by a Vega of .05 per tick gives us a value of $.20. Next, we subtract $.20 from the June 70 option's present value of $2.00 and we get a value of $1.80 at 36 volatility. Now the two options are valued at an equal volatility basis.

Looking at this first adjustment where we moved the June 70's volatility down to 36 from 40, we have a value of $1.80 at 36 volatility. The August 40 call has a value of $3.00 at 36 volatility. The spread will be worth $1.20 at 36 volatility.

If you wanted to move the August 70 calls instead, you would take the August 70 call Vega of .08 and multiply it by the four tick implied volatility difference. This gives you a value of $.32 that we must add to the August 70 call's present value in order to bring it up to an equal volatility (40) with the June 70 call. Adding the $.32 to the August 70 call will give it a $3.32 value at the new volatility level of 40, which is the same volatility level as the June 40 calls. Now, our spread is worth $1.32 at 40 volatility. August 70 calls at $3.32 minus the June 70 calls at $2.00 gives the price of the spread at 40 volatility.

It does not make any difference which option you move. The point is to establish the same volatility level for both options. Then you are ready to compare apples to apples and options to options for an accurate spread value and volatility level.

Since we now have an equal base volatility, we can calculate the spread's Vega by taking the difference between the two individual option's Vegas. In the example above, the spread's Vega is .03 (.08 - .05). The Vega of the spread is calculated by finding the difference between the Vega's of the two individual options because in the time spread, you will be long one option and short the other option.

As volatility moves one tick, you will gain the Vega value of one of the options while simultaneously losing the Vega value of the other. The spread's Vega must be equal to the difference between the two options Vega's, so, our spread is worth $1.20 at 36 volatility with a .03 Vega or $1.32 at 40 volatility with a .03 Vega.

Going back to our original spread value of $1.00 with a Vega of .03, we can now calculate the volatility of that spread. We know the spread is worth $1.20 at 36 volatility with a Vega of .03. Therefore, we can assume that the spread trading at $1.00 must be trading at a volatility lower than 36.

To find out how much lower we first take the difference between the two spread values, which is $.20 ($1.20 at 36 volatility minus $1.00 at ? volatility). Then we divide the $.20 by the spread's Vega of .03 and we get 6.667 volatility ticks. We then subtract 6.667 volatility ticks from 36 volatility and we get 29.33 volatility for the spread trading at $1.00.

We can also determine the volatility of the spread as the spread's price changes. We will fix the spread price at $1.30. To calculate this, we must first take the value of the spread ($1.20 at 36 volatility) and find the dollar difference between it and the new price of the spread ($1.30). The difference is $.10. The Vega of the spread must now divide this dollar difference. The $.10 difference divided by the .03 Vega gives you a value of 3.33 volatility ticks. Then add the 3.33 ticks to the 36 volatility and you get 39.33 as the volatility for the spread trading at $1.30.

Let us double-check our work by calculating the volatility the other way. This time we will do the calculation by moving the August 70 calls up to the equal base volatility of the June 70 calls. As calculated earlier, the August 70 calls will have a value of $3.32 at 40 volatility. The June 70 calls are worth $2.00 at 40 volatility, so the spread is worth $1.32 at 40 volatility.

Now, move the spread price to $1.30, $.02 lower than the value of the spread at 40 volatility. As before, we take the difference in the prices of the spread. The result is $.02 ($1.32 - $1.30). Then, divide $.02 by our spread's Vega of .03 (remember that the Vega of the spread is equal to the difference between the Vega of the two individual options). $.02 divided by .03 gives us a value of .67. We must subtract that .67 from our base volatility of 40. That gives us a 39.33 (40 - .67) volatility for the spread trading at $1.30. This volatility matches our previous calculation perfectly.

At first glance, you might be wondering why we went through all of these calculations. With the June 70 calls at 40 volatility, price $2.00, Vega .05 and the August 70 calls at 36 volatility, price $3.00, Vega .08 why not just take an average of the volatility? This would give us a 38 volatility for the spread with a price of $1.00 when in actuality $1.00 in the spread represents a 29.33 volatility.

This would be almost a nine-tick difference, which represents a whopping 30% mistake! As stated earlier, Vega is not linear. You cannot weigh each month evenly and just take an average of the two months. For argument's sake suppose you did. Let's say you found the difference of the Vegas of the options and came up with a spread Vega of .03, which is correct. However, when you try to calculate the spread's volatility and price you would have difficulty.

Now, recalculate the spread with the trading price of $1.30, or $.30 higher than your value at 38 volatility. Divide that $.30 higher difference by the spread's Vega of .03. You get a 10-tick volatility increase. Add that increase to the base 38 volatility. That would mean you feel the spread is trading at 48 volatility instead of a 39.33 volatility! This type of mistake could be very, very costly. Remember, apples to apples, oranges to oranges. It does not matter which option's volatility of the spread you move as long as you get both options to an equal base volatility.

Ron Ianieri enjoyed 14 years of experience as a floor trader on the Philadelphia Stock Exchange, including four years as the lead market maker in DELL computer options one of the busiest books in history. He is currently chief options strategist and co-founder of The Options University, an educational company that teaches investors how to make consistent profits using options while limiting risk.Sitemap
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