Part 2: Time / Diagonal Spreads & Future Option Trading

We can also determine the volatility of the future option trading spread as the spread’s price changes. Let’s fix the spread price at $1.30. To calculate this, we must first take the value of the future option trading 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 future option trading at $1.30.

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.

Now, recalculate the spread with the future option trading price of $1.30, or $.30 higher than your value at 38 volatility. Divide that $.30 higher difference by the future option trading 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 future option 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 doesn’t matter which option’s volatility of the spread you move as long as you get both future option trading to an equal base volatility.