The Oil Drum

161 comments on How Periodic Are the Oil Price Fluctuations?

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Khebab on September 23, 2006 - 9:51am

Thanks for the link Halfin! the Black-Scholes model is truly a beautiful model!

If I look at the lognormal distribution properties:

the variable mu is a linear dependent function of time in my case (log(Price)= 0.2615*(t-2002)+3.1). We have the following relationship for the mean and the variance of lognormal distributed variable X:

so the standard deviation is proportional to the mean. The coefficient in my case would be sqrt(exp(0.091^2)-1)= 0.0912= 9.1% wich is not far from the 6% you are using. So volatility would be given by the following function:

0.0912 * exp(0.2615*(t-2002)+3.1 + 0.091^2/2)

using this formula for mid-September 2006, we get a volatility between $6.89 and $7.03. The 95% confidence interval would be [$61.2, $89.2]. The recent drop of $22 is 22/75.2= 22.6% which is 22.6/9.3= 2.43 SD. The move toward $85 would be 3.44 SD with my value.

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Bigelow on September 23, 2006 - 11:07am

So you are still saying highly unusual moves. (?)

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obdacher on September 23, 2006 - 2:34pm

I stick to my square root: this is the random walk hypothesis: Rather than cruising at a constant speed such that the position deviates proportionally with time, a random walk is erratic with steps in both directions: positive and negative. Since steps have random +/- signs, their square is always positive, and thus the sum of squares of the steps is increasing in proportion to time.