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

I am doing research on uncertainty analysis and risk assessment for oil field development. For doing economic forecast and valuation I use Real Options theory, which is almost similar to theory used in finance. RO theory is used for valuation of a real, tangible asset etc. My question is as follow:

I have forecast of future cash flows for 20 years from my reservoir, which I get from flow rates and oil price. The flow rates came from Monte Carlo simulation. I compute Present Value (PV) from these future cash flows. In order to use Real Option Valuation (ROV), using Black-Scholes equation, I must know the volatility of the economic returns for 20 years from my reservoir. Knowing this information what could be the appropriate measure of computing volatility of the economic returns from my reservoir?

I have heard of stochastic volatility in finance, however as I am not sure how appropriate it would be to use the stochastic volatility in my case.

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
@Shane: I didn't devise the term 'real'. If you search for it then you'll find that its a concept borrowed from quant finance for use in assets other than just stock and derivatives. Hence, the term real. Also, not all the concepts of finance can be used here because of the difference in fundamental premise and assumptions. – Pupil Feb 6 '11 at 3:15
@Dimitris: What's your comment about? – Pupil Feb 6 '11 at 3:17
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

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 from my reservoir?

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