To be able to calculate the volatility of the spread, we must
equalize the volatilities of the individual options.

First, lets move the June calls by moving Junes 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 options 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 70s
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. 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 calls 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
spreads vega by taking the difference between the two
individual options vegas. In the example above, the spreads
vega is .03 (.08 - .05). The vega of the spread is calculated by
finding the difference between the vegas 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. Thus the spreads vega must be equal to the
difference between the two options 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 spread.

We know the spread is worth $1.20 at 36 volatility with a vega
of .03. So, 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
spreads 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
spreads price changes. Lets 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. This dollar difference must now be divided by the vega of
the spread. 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.

Lets 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. Thus the
spread is worth $1.32 at 40 volatility.

Now lets again 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 spreads 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 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! Because, as stated earlier, vega is not
linear; you can not weigh each month evenly and just take an
average of the two months. For arguments sake suppose you did.
Lets 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 spreads 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 spreads 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 doesnt matter which options volatility of the
spread you move as long as you get both options to an equal base
volatility.