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Distribution
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The probability distribution of a variable describes the probability of the variable attaining a certain value. Assumptions about the distribution of the Underlying are crucial to Option models because the distribution determines how likely it is that the Option Will be exercised. Many models assume the logarithm of the relative return has a normal distribution, which can be described by two parameters. The first is the distribution’s mean; the second its standard deviation (equivalent, if annualised, to Volatility). In practice, most empirically observed asset distributions depart from normality. This departure can be described in terms of the Skew (how much it tilts to one side or the other) and kurtosis, which describes how fat or thin are the tails at either side. Most markets tend to have Fat tails (to be leptokurtic)rather than thin tails (platykurtic). This pushes up the price of Out-of-the-money options.
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Privatebanking.com
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