We can also determine the volatility of the
future option trading 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 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.
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 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 lets 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 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
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 arguments
sake suppose you did. Lets 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
spreads 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 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 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 doesnt
matter which options volatility of the spread you move as long
as you get both future option trading to an equal base volatility.