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The elasticity at a point is the limit of the arc elasticity between two points as the separation between those two points approaches zero. The concept of elasticity is widely used in economics and metabolic control analysis (MCA); see elasticity (economics) and elasticity coefficient respectively for details.
In mathematical finance, the CEV or constant elasticity of variance model is a stochastic volatility model, although technically it would be classed more precisely as a local volatility model, that attempts to capture stochastic volatility and the leverage effect.
Firstly, if the true population mean is unknown, then the sample variance (which uses the sample mean in place of the true mean) is a biased estimator: it underestimates the variance by a factor of (n − 1) / n; correcting this factor, resulting in the sum of squared deviations about the sample mean divided by n-1 instead of n, is called ...
Starting from a constant volatility approach, assume that the derivative's underlying asset price follows a standard model for geometric Brownian motion: = + where is the constant drift (i.e. expected return) of the security price , is the constant volatility, and is a standard Wiener process with zero mean and unit rate of variance.
It is also the continuous distribution with the maximum entropy for a specified mean and variance. [18] [19] Geary has shown, assuming that the mean and variance are finite, that the normal distribution is the only distribution where the mean and variance calculated from a set of independent draws are independent of each other. [20] [21]
The Rayleigh–Ritz method for solving boundary-value problems in elasticity and wave propagation; Fermat's principle in geometrical optics; Hamilton's principle in classical mechanics; Maupertuis' principle in classical mechanics; The principle of least action in mechanics, electromagnetic theory, and quantum mechanics; The variational method ...
To find a second-order approximation for the covariance of functions of two random variables (with the same function applied to both), one can proceed as follows.
Elasticity is the measure of the sensitivity of one variable to another. [10] A highly elastic variable will respond more dramatically to changes in the variable it is dependent on. The x-elasticity of y measures the fractional response of y to a fraction change in x, which can be written as