1QuantLib::GenericRiskStatistics(3) QuantLib QuantLib::GenericRiskStatistics(3)
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NAME

6       QuantLib::GenericRiskStatistics -
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8       empirical-distribution risk measures
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SYNOPSIS

12       #include <ql/math/statistics/riskstatistics.hpp>
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14       Inherits S.
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16   Public Types
17       typedef S::value_type value_type
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19   Public Member Functions
20       Real semiVariance () const
21       Real semiDeviation () const
22       Real downsideVariance () const
23       Real downsideDeviation () const
24       Real regret (Real target) const
25       Real potentialUpside (Real percentile) const
26           potential upside (the reciprocal of VAR) at a given percentile
27       Real valueAtRisk (Real percentile) const
28           value-at-risk at a given percentile
29       Real expectedShortfall (Real percentile) const
30           expected shortfall at a given percentile
31       Real shortfall (Real target) const
32       Real averageShortfall (Real target) const
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Detailed Description

35   template<class S> class QuantLib::GenericRiskStatistics< S >
36       empirical-distribution risk measures
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38       This class wraps a somewhat generic statistic tool and adds a number of
39       risk measures (e.g.: value-at-risk, expected shortfall, etc.) based on
40       the data distribution as reported by the underlying statistic tool.
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42       Possible enhancements
43           add historical annualized volatility
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45       Examples:
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47       DiscreteHedging.cpp.
48                                                                        ight].

Member Function Documentation angle

50   Real semiVariance () const returns the vaarnigalnec)e^2of;|o;bsxer<vagtlieonxs below the
51       mean, ac{N}{N-1} thrm{E}t[ (x-gle x
52       ]
53       See Markowitz (1959).
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55   Real semiDeviation () const returns the semi deviation, defined as the
56       square root of the semi variance.
57   Real downsideVariance () const returns the viagrhita]n.ce] of observations below
58       0.0, ac{N}{N-1} thrm{E}t[ x^2 ;|; x < 0
59   Real downsideDeviation () const returns the downside deviation, defined as
60       the square root of the downside variance.
61   Real regret (Real target) const returns the varianceigohft]o.bs]ervations below
62       target, ac{N}{N-1} thrm{E}t[ (x-t)^2 ;|; x < t
63       See Dembo and Freeman, 'The Rules Of Risk', Wiley (2001).
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65   Real potentialUpside (Real centile) const
66       potential upside (the reciprocal of VAR) at a given percentile
67       Precondition:
68           percentile must be in range [90-100%)
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70   Real vaglueAtRisk (Real centile) const
71       valiue-at-risk at a given percentile Precondition:
72         n percentile must be in range [90-100%)
73         {
74   Real exapectedShortfall (Real centile) const
75       exprected shortfall at a given percentile returns the expected loss in
76       casre that the loss exceeded a VaR threshold,
77         a                              ight], ].PP that is the average of
78       thrym{E}t[ x ;|; x < thrm{VaR}(p)
79       obs}ervations below the given percentile $ p $. Also know as conditional
80       val{ue-at-risk.
81         l
82       Seel Artzner, Delbaen, Eber and Heath, 'Coherent measures of risk',
83       Mat}hematical Finance 9 (1999)
84         1
85       Pre&condition:
86         x percentile must be in range [90-100%)
87         <
88   Real shtortfall (Real target) const probability of miigshsti]ng] twhheergeivTehnettaa(rxg)et=,
89       def0ined as thrm{E}t[ Theta ;|; (-infty,infty)
90       t &
91   Real axverageShortfall (Real tairgghett])]const averaged shortfallness, defined
92       asqthrm{E}t[ t-x ;|; x<t

Author t

94       Ge\nerated automatically by Doxygen for QuantLib from the source code.
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98Version 1a.0.1                   Thu Aug 19 20Q1u0antLib::GenericRiskStatistics(3)
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