# Options Trading Lessons: Using 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- 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.

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- 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.

About the Author

Ron Ianieri is currently Chief Options Strategist at The Options University, an educational company that teaches investors how to make consistent profits using options while limiting risk. For more information please contact The Options University at http://www.optionsuniversity.com or 866-561-8227

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