semiDeviation (3) - Linux Manuals

semiDeviation: empirical-distribution risk measures

NAME

QuantLib::GenericRiskStatistics - empirical-distribution risk measures

SYNOPSIS

#include <ql/math/statistics/riskstatistics.hpp>

Inherits S.

Public Types

typedef S::value_type value_type

Public Member Functions

Real semiVariance () const

Real semiDeviation () const

Real downsideVariance () const

Real downsideDeviation () const

Real regret (Real target) const

Real potentialUpside (Real percentile) const
potential upside (the reciprocal of VAR) at a given percentile
Real valueAtRisk (Real percentile) const
value-at-risk at a given percentile
Real expectedShortfall (Real percentile) const
expected shortfall at a given percentile
Real shortfall (Real target) const

Real averageShortfall (Real target) const

Detailed Description

template<class S> class QuantLib::GenericRiskStatistics< S >

empirical-distribution risk measures

This class wraps a somewhat generic statistic tool and adds a number of risk measures (e.g.: value-at-risk, expected shortfall, etc.) based on the data distribution as reported by the underlying statistic tool.

Possible enhancements

add historical annualized volatility

Examples:

DiscreteHedging.cpp.

Member Function Documentation

Real semiVariance () const

returns the variance of observations below the mean, [ ac{N}{N-1} mathrm{E}

---

)^2 ;|; x <

---

ngle ight]. ]

See Markowitz (1959).

Real semiDeviation () const

returns the semi deviation, defined as the square root of the semi variance.

Real downsideVariance () const

returns the variance of observations below 0.0, [ ac{N}{N-1} mathrm{E}

---

al downsideDeviation () const"

returns the downside deviation, defined as the square root of the downside variance.

Real regret (Real target) const

returns the variance of observations below target, [ ac{N}{N-1} mathrm{E}

---

e Dembo and Freeman, 'The Rules Of Risk', Wiley (2001).

Real potentialUpside (Real centile) const

potential upside (the reciprocal of VAR) at a given percentile

Precondition:

percentile must be in range [90-100%)

Real valueAtRisk (Real centile) const

value-at-risk at a given percentile

Precondition:

percentile must be in range [90-100%)

Real expectedShortfall (Real centile) const

expected shortfall at a given percentile

returns the expected loss in case that the loss exceeded a VaR threshold,

[ mathrm{E}

---

average of observations below the given percentile $ p $. Also know as conditional value-at-risk.

See Artzner, Delbaen, Eber and Heath, 'Coherent measures of risk', Mathematical Finance 9 (1999)

Precondition:

percentile must be in range [90-100%)

Real shortfall (Real target) const

probability of missing the given target, defined as [ mathrm{E}

---

ta ;|; (-infty,infty) ight] ] where [ Theta(x) =

---

al averageShortfall (Real target) const"

averaged shortfallness, defined as [ mathrm{E}

---

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