 Provided By Options University

#### How To Calculate The Volatility Of The Future Option Trading Spread?

To be able to calculate the volatility of the spread, we must equalize the volatilities of future option trading.

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 commodity option trading value of \$2.00 and we get a value of \$1.80 at 36 volatility. Now we find the two future option trading at an equal volatility basis.

Looking at this first adjustment where we moved the June 70s volatility down to 36 from 40, we find our future option trading at a value of \$1.80 at 36 volatility. The August 40 call has a value of \$3.00 at 36 volatility. So 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 must be added 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 we find our future option trading at \$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 future option trading 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 future option trading 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 future option trading while simultaneously losing the vega value of the other. Thus the spreads vega must be equal to the difference between the two future option trading vegas. 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 future option trading spread.

We know the future option trading spread is worth \$1.20 at 36 volatility with a vega of .03. So, we can assume that the spread future option 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 future option trading values, which is \$.20 (\$1.20 at 36 volatility minus \$1.00 at? volatility). Then we divide the \$.20 by the commodity option trading 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 future option trading at \$1.00.

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