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Submitted By Kodwo

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Words 618

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Wednesday, December 03 - 2008 at 12:10

Prices move up and down; all the time. Sometimes a little, but every now and then by large amounts. The measurement for these movements is called volatility, and is measured using standard deviation.

Volatility is the most important price driver of option premiums.

We are interested in future volatility. However, this is the only kind of volatility that we cannot know. We are able to calculate historical volatility, but is this a good bias for future volatility?

Every option pricing model tries to evaluate options by ascribing probabilities to several different possible prices of the underlying value at expiry.

Because the distribution of prices occurs in the future, and every underlying value has its own characteristics, there is no clear answer to the question of how probabilities must be allocated. But, as an approximation, most models (some with adjustments) start with the assumption of a normal distribution.

A normal distribution curve is always defined by two things: the average or mean (reflected by the spike in the figure below) and the standard-deviation (the speed of expansion of the curve).

The standard deviation can also be interpreted in terms of a probability of an occurrence. Once you know a certain mean and standard deviation, it is always possible to calculate the probability of an occurrence within a certain range of the mean.

Usually you need a table of standard deviations (SD) to calculate exactly. However, option-traders use the following approximations:

• Plus or minus 1 SD of the mean includes 68.3% (approximately 2/3) of all possible results.

• Plus or minus 2 SD of the mean includes 95.4% (around 19/20) of all possible results.

• Plus or minus 3 SD of the mean includes 99.7% (roughly 369/370) of all possible...

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