Provided By Options University

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

Lets 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 future option trading value of \$3.32 at 40 volatility.

The June 70 calls are worth \$2.00 at 40 volatility. Thus the future option trading spread is worth \$1.32 at 40 volatility.

Now lets again move the spread price to \$1.30, \$.02 lower than the value of the future option trading spread at 40 volatility. As before, we take the difference in the prices of the future option trading 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. That .67 must be subtracted from our base volatility of 40. That gives us a 39.33 (40 - .67) volatility for the spread future option 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 for our future option trading ventures. 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 future option trading 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 in the future option trading, which represents a whopping 30% mistake! Because, 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 future option trading 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.

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