# Appropriate measure of Volatility for economic returns from an asset?

In order to use Real Option Valuation (ROV), using Black-Scholes equation, I must know the volatility of the economic returns for T years. Knowing this information what could be the appropriate measure of computing volatility of the economic returns from my reservoir?

The distribution of PV for any particular year is coming out to be gaussian. There is no historical data known.

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Not a fan of the "real" tag here. What's intended? Realized volatility or a real, physical commodity? – Shane Feb 5 '11 at 23:45
Possibly "real option". – Dimitris Feb 6 '11 at 1:34
Is the standard deviation of the PV of year X proportional to the square root of X? If not, Black-Scholes will only work if volatility is itself a function of time. It might be easier to just list the means and standard deviations (of the returns, not the PV) for each year? – barrycarter Feb 6 '11 at 3:33
@Harpeet That's a fair point; I raised this on meta: meta.quant.stackexchange.com/questions/35/… – Shane Feb 6 '11 at 14:09
If volatility is a function of time, B-S is probably not the best estimator. B-S was derived w/ fixed volatility in mind. It can be used w/ variable volatility, but if volatility changes a lot, it's not the best fit. – barrycarter Feb 6 '11 at 20:51

I think this has something to do with my question ("Black Equivalent Volatility"). I just realized that the answer might be your question:

Knowing this information what could be the appropriate measure of computing volatility of the economic returns?

In Energy Markets, like oil and electricity, one model we use is the mean reversion in the natural log of the spot prices.

$$d(ln(S)) = a(b-ln(S))de + vdz$$ where:

$S$ = spot price

$t$ = time of observation

$a$ = rate of mean reversion

$v$ = volatility

$b$ = long-term equilibrium

$dz$ = random stochastic variable

Now there are books that would show you how to solve for the volatility in that equation but i think the best one for me is Dragana Pilipovic's book entitled "Energy Risk 2nd Ed" (chapter 5, page 108)

And I think the black-equivalent volatility is a short-form equation that you can use off the bat. So here is my answer to your question:

black-equivalent volatility = volatility x $\sqrt{(1-e^{-2aT})/2aT }$

where:

$T$ = period of time (20 years)

$a$ = rate of mean reversion

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