McSimulation_Extra_Data

Refers to the output of QuantLib's

Returns the array of sample final values and their respective weights in the context of a monte carlo algorithm.

Refers to the output of QuantLib's

Returns the error estimate on the mean value in the context of a monte carlo algorithm, defined as σ/n, where σ is the standard deviation and n² = N with N being the number of samples.

Refers to the output of QuantLib's

Returns the downside deviation in the context of a monte carlo algorithm, defined as the quare root of the downside variance.

Refers to the output of QuantLib's

Returns the downside variance in the context of a monte carlo algorithm, defined as N/(N-1)<θ(x-<x>)²>, where N is the number of samples, <x> is the mean of the sample values xi, θ equals 1 if x-<x> is negative and otherwise equals 0, which means that <θ(x-<x>)²> is the mean of the squared negative distances from the mean (xi-<x>)², such that xi-<x> < 0.

Refers to the output of QuantLib's

of the 4th power of the distances from the mean (xi-<x>)^4 and σ is the standard deviation.

The above evaluates to 0 for a Gaussian distribution.

Refers to the output of QuantLib's

Returns the maximum sample value in the context of a monte carlo algorithm.

Refers to the output of QuantLib's

Returns the mean in the context of a monte carlo algorithm, defined as Sum{ wi*xi } / Sum{ wi }, where wi are the weights and xi the sample values.

Refers to the output of QuantLib's

Returns the minimum sample value in the context of a monte carlo algorithm.

Refers to the output of QuantLib's

Returns the number of samples in the context of a monte carlo algorithm.

Refers to the output of QuantLib's

Returns the skewness in the context of a monte carlo algorithm, defined as N²/[(N-1)(N-2)] n<(x-<x>)³>/σ³, where n = N²/[(N-1)(N-2)], N is the number of samples, <x> is the mean of the sample values xi and <(x-<x>)³> is the mean of the cubed distances from the mean (xi-<x>)³ and σ is the standard deviation.

The above evaluates to 0 for a Gaussian distribution.

Refers to the output of QuantLib's

Returns the standard deviation in the context of a monte carlo algorithm, defined as the square root of the variance.

Refers to the output of QuantLib's

Returns the variance in the context of a monte carlo algorithm, defined as N/(N-1)<(x-<x>)²>, where N is the number of samples, <x> is the mean of the sample values xi and <(x-<x>)²> is the mean of the squared distances from the mean (xi-<x>)².

Refers to the output of QuantLib's

Returns the sum of the weights in the context of a monte carlo algorithm.