To be able to calculate the volatility of the spread, we must
equalize the volatilities of future option trading.
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 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 70s
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 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 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 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 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 spreads 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 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
future option trading at $1.00.