How do I use forward volatility?

Let's illustrate the answer with a detailed example using Excel.

Forward Volatility. Forward volatility is similar to implied volatility. It can be used in much the same way implied volatility as an input into a value at risk or other risk management system. It is limited to the time period before the start of delivery. So, the forward volatility for April terminates at the end of March. Besides risk systems, we can also use it to make statements about the likelihood of something in the future.

Context: Please refer to the pdf sample or the sample clip on the website for the context details. Today is September 18, 2008 and we are in CT Zone in ISO-NE (Connecticut) . The forward Power Nominals valuation for January 2009 is $112.42 and the forward volatility for January is 40.2%.

Problem: What is the likelihood that CT Zone will be above $130 at the start of delivery? Below $100.00?

Forward Volatility = FVol

≈ Implied Volatility = Ivol

= 0.402 = 40.2%

DeliveryDate

= First day of contract delivery = DeliveryDate()

= Jan 1, 2009

[Note: Technically, should be the date as of which the option expires from which we extracted the forward volatility. However, we do not have such a date.]

AsofDate

= Sep 18, 2008

DaysLeft

= DeliveryDate - AsofDate

= 105

De-annualized percentage stdev = Vol

= EXP(Ivol/SQRT(365/DaysLeft)

= EXP(0.402/SQRT(365/105))

= 1.2406 = 24.06%

PriceAsof = Today’s price

= $112.42

PriceUp

= $130.00

PriceRelative =

PR = LN(PriceUp/PriceAsof)

= LN(130/112.42)

= 0.145 = Up 14.5%

Probability Price > $130.00?

= 1 - NORMDIST(PR,  0, Vol, TRUE)

= 1 - NORMDIST(0.145, 0 ,0.2406, TRUE)

= 0.273 = 27.3%

Conclusion: The probability that CT Zone for January will be priced $130.00 or more at the end of December is 27.3%.

What is the likelihood that the price will be below $100.00?

PriceRelative = PR = LN(PriceDn/PriceAsof)

= LN(100/112.42)

=  -0.117 = Down 11.7%

Probability (Price < $100.00)

= NORMDIST(-0.117, 0, 0.2406, TRUE)

= 0.313 = 31.3%

Conclusion: The probability that CT Zone for January will be priced less than $100.00 at the end of December is 31.3%