# How to Calculate the Volatility of the Spread in Options Trading

August 14, 2010 by admin

Filed under Option Trading

In order to be able to calculate the volatileness of propagaciÃ ³ n, we must equal volatilenesses of the options individuales.& #13; First of all, we are going to move of June of calls being moved the implÃcita volatileness of June by 40 to 36, one disminuciÃ ³ n of four garrapatas volatileness. Four volatileness of the garrapatas, multiplied by a fertile valley of. 05 by tick give a value us of $. 20. To continuaciÃ ³ n we reduced $. 20 of June the present value of 70 opciÃ ³ n of $ 2. 00 and obtains a 36 value of $ 1. 80 to volatileness. Now the two options are evaluated in a base volatileness igual.& #13; As far as this first adjustment in which trasladÃ ³ the 70 of June of volatileness up to 36 from 40, we have a value of $ 1. 80 to 36 volatileness. 40 August call volatileness has a value of $ 3. 00 to 36. Therefore propagaciÃ ³ n valdrÃ$ 1. 20 to 36 volatilidad.& #13; If you want to move August 70, solicits that, you tomarÃa the fertile valley August of call of 70. 08 and multiply by four the difference of implÃcita volatileness of garrapatas.& #13; This gives a value him of $. 32 that must be aÃ±adir to the present value of August of 70 calls with the purpose of to take it until an equal volatileness (40) with 70 June of call. To add $. 32 to 70 of August of call give to 3 dÃ ³ him lares. Value of 32 in the level of volatileness of the new ones of 40 that is the same level of volatileness that June 40 llamadas.& #13; Now, ours expansiÃ ³ n is a value of $ 1. 32 to 40 volatileness. August 70 calls of $ 3. 32 except 70 June to two the calls of dÃ ³ lares. 00 to fix the price of propagaciÃ ³ n to 40 volatilidad.& #13; ³ n does not make any difference of opciÃ that to move. The point is to establish the same level of volatileness for both options. Then already estÃready to compare apples with apples and the options to the options for a value of propagaciÃ exact ³ n and level of volatilidad.& #13; Since now we have an equal base of volatileness, we can calculate propagaciÃ ³ n of fertile valley taking the difference between opciÃ ³ n from two fertile valleys individual. In the previous example, propagaciÃ ³ n fertile valley is. 03 (. 08 -. 05). The fertile valley of propagaciÃ ³ n calculates finding the difference between those of the fertile valley of the two individual options, because in the time of propagaciÃ ³ n, that pasarÃlong time one opciÃ ³ n and cuts the other opciÃ ³ n.& #13; As volatileness moves a garrapata, you ganarÃthe value of fertile valley one of the options at the same time of losing the value fertile valley of the other. Therefore propagaciÃ ³ n of fertile valley must be equal to the difference between the fertile valley of two options. Therefore, ours expansiÃ ³ n is a value of $ 1. 20 to 36 with a volatileness. 03 fertile valley or $ 1. 32 to 40 with a volatileness. 03 vega.& #13; Returning to our value difusiÃ original ³ n of $ 1. 00 with a fertile valley from. 03, now we can calculate the volatileness of which propagan.& #13; We know the difference is a value of $ 1. 20 to 36 of volatileness with a fertile valley of. 03. Therefore, we can suppose that the commerce of difusiÃ ³ n from $ 1. 00 deberÃto develop a commercial activity in a volatileness smaller than 36.& #13; In order to know cuÃnto mÃs under is in the first place to take care of the difference both enters values extended and that is of $. 20 ($ 1. 20 to 36 volatileness less $ 1. 00 a? Volatileness). Soon we divided $. 20 by fertile valley propagaciÃ ³ n of. 03 and we obtain 6. 667 garrapatas volatileness. To continuaciÃ ³ n, to reduce 6. 667 garrapatas volatileness of the volatileness of 36 and we have 29. 33 of volatileness for the commerce of difusiÃ ³ n from $ 1. 00.& #13; TambiÃ©n can determine the volatileness of propagaciÃ ³ n like changes of prices of propagaciÃ ³ n. We are going to fix the price of difusiÃ ³ n from $ 1. 30. In order to calculate this, first we must have the value of propagaciÃ ³ n ($ 1. 20 to 36 volatileness) and of finding the difference in dÃ ³ lares between Ã©ste and the new price of propagaciÃ ³ n ($ 1. 30). The difference is of $. 10. This difference in dÃ ³ lares now is divided by the fertile valley of the differential. $. 10 divided by the difference. 03 fertile valley gives to a value of 3. 33 garrapatas volatileness him. Soon one adds the 3. 33 garrapatas to the volatileness of 36 and propagaciÃ is obtained 39. 33 like the volatileness of the interchanges ³ n from $ 1. 30.& #13; Double-Go to verify our work by means of cÃlculo of the volatileness of the other manera.& #13; This time we are going to do cÃlculo moving the August 70 calls to the volatileness of the base of the June equality 70 calls. SegÃºn the calculated thing previously, the August 70 calls tendrÃa value of $ 3. 32 to 40 volatilidad.& #13; The June 70 two calls are worth dÃ ³ lares. 00 to 40 volatileness. AsÃ, the difference is a value of $ 1. 32 to 40 volatilidad.& #13; Now we are going to move the new price extendiÃ ³ to $ 1. 30, $. 02 mÃlow s that the value of propagaciÃ ³ n to 40 volatileness. Like before, we took the difference in the prices from propagaciÃ ³ n. The result is $. 02 ($ 1. 32 – $ 1. 30). Then, it divides $. 02 by fertile valley ours expansiÃ ³ n of. 03 (it remembers that the fertile valley of propagaciÃ ³ n is equal to the difference between the fertile valley of the two individual options). $. 02 divided by. 03 give a value us of. 67. That. 67 the volatileness of our base of 40 is due to remain. That gives 39 us. 33 (40 -. 67) the volatileness of the interchanges propagaciÃ ³ n from $ 1. 30. This volatileness responds ours cÃlculo previous to perfecciÃ ³ n.& #13; Perhaps at first sight, it is asked for quÃ© we went to travÃ©s of all these cÃlculos. With the June 70 calls to 40 volatileness, the two price of dÃ ³ lares. 00, fertile valley. 05 and 70 of August to the 36 calls of volatileness, the three price of dÃ ³ lares. 00, fertile valley. 08 Âby quÃ© not to have an average of volatileness? This us darÃa a volatileness 38 for difusiÃ ³ n with a price of $ 1. 00 when in fact $ 1. 00 in extensiÃ ³ n represent 29. 33 volatilidad.& #13; This serÃa almost nine by garrapatas ones difference that represents a friolera error of 30%! Because, as it were said previously, Fertile valley is not linear, every month of way cannot be weighed uniforms and finishes both taking an average from months. By the love of argument to suppose it did that it. We say that you find the difference of fertile valleys of the options and came above for with one propagaciÃ ³ n of the fertile valley. 03 that is the correct one. Nevertheless, when ³ n tries to calculate the volatileness of propagaciÃ and the price that tendrÃan dificultades.& #13; Now, ³ n with the price of cotizaciÃ returns to calculate propagaciÃ ³ n of $ 1. 30, or $. 30 mÃhigh s that its value in 38 volatileness. It divides that $. 30 fertile valley differentiates superior in difusiÃ ³ n from. 03. You obtain an increase of 10 by garrapatas volatileness. AÃ±ade that increases to base 38 volatileness. That means that you feel propagaciÃ ³ n negotiates to 48 volatileness instead of 39. 33 volatileness! This type of error podrÃa to be very, very expensive. It remembers, apples with apples, oranges with oranges. It does not matter that volatileness opciÃ ³ n of propagaciÃ ³ n to move the time as both options for a volatileness of the equality base.

# Options Trading Lessons: Using Base Volatility

August 14, 2010 by admin

Filed under Option Trading

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.