kupiec paul - techniques for verifying the accuracy of risk measurement models

8/19/2019 Kupiec Paul - Techniques for Verifying the Accuracy of Risk Measurement Models

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TECHNIQUES FOR VERIFYING

THE ACCURACY

RISK

MEASUREMENT

MO E

Paul

H

Kupiec

is a senior economist with the Board Governors of the

Federal Reserve System

in Washington, D.C.

Risk

exposures

are

typically

quantified in terms a

value

at risk IiflR estimate. A UlR estimate corresponds

to a specific critical

value

of a porifolio s

potential

one-day

profit and

loss

probability distribution.

Given

their function

both as

internal

risk management

tools

and as potential

reg

ulatory measures risk exposure, it is important to quantify

the accuracy

an institution s UlR estimates.

This study

shows

that the formal

statistical

proce

dures that would typically be used in performance-based

UlR

verification

tests require

large

samples

to

produce

a

reli-

T

hi s study

considers alternative

statistical

techniques that could be used to verify the

accuracy

of

estimates

of

the tail values

of

the distribution

of

potential gains and losses

for a por tfol io

of

securities, futures, and derivative

positions. These so-called reality checks have

been

advanced as a tool for determining the accuracy

of

risk exposure estimates generated by risk measure

ment models.

able

assessment

of a

model s

accuracy

and likelihood of very

low

probability

test statistics based on historical

tradi

have

very poor power in small samples,

possible for a bank orits supervisor to

a UlR estimate unless many

years

available.

Historical simulation-based v

tics also require long

samples

to gene

Estimates 0 01 critical

values

exhi

even

in

samples

as large

as

ten years

A VaR estimate corresponds

cal value of a portfolio's potential

loss probability distribution. Typica

is defined to be a loss large enough

bility that the portfolio could post

most some specified value, like 1

VaR measure thus corresponds to

critical value

of

the portfolio's po

loss distribution.

T h e J

o u r n a l o f D e r i v a t i v e s 1 9 9 5 . 3 . 2 : 7 3 - 8 4 . D o w n l o a d e d f r o m w

w w . i

i j o u r n a l s . c o m

b y A b e l G a r c i a o n 0 8 / 0 9 / 1 2 .

I t i s i l l e g a l t o m a k e

u n a u t h o r i z e d c o p i e s o f t h i s a r t i c l e ,

f o r w

a r d t o a n u n a u t h o r i z e d u s e r o r t o p o s t

e l e c t r o n i c a l l y w i t h o u t P u b l i s h e r p e r m i s s i o n .


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T h e J o u r n a l o f D e r i v a t i v e s 1 9 9 5 . 3 . 2 : 7 3 - 8 4 .

D o w n l o a d e d f r o m w

w w . i

i j o u r n a l s . c o m b

y A b e l G a r c i a

o n 0 8 / 0 9 / 1 2 .

I t i s i l l e g a l t o m a k e u n a u t h o r i z e d c o p i e s o f t h i s a r t i c l e ,

f o r w a r d t o a n u n a u t h o r i z e d u s e r o r t o p o s t e l e c t r o n i c a l l y w i t h o u t P u b l i s h e r p e r m i s s i o n .


3/12



w w . i



o n 0 8 / 0 9 / 1 2 .


f o r w a r d t o a n u n a u t h o r i z e d u s e r o r t o p o s t e l e c t r o n i c a l l y w

i t h o u t P u b l i s h e r p e r m i s s i o n .


4/12



w w . i



o n 0 8 / 0 9 / 1 2 .





5/12



w w . i



o n 0 8 / 0 9 / 1 2 .





6/12



w w . i


y A b e l G a r c i a o n 0 8 / 0 9 / 1 2 .

I t i s i l l e g a l t o

m a k e u n a u t h o r i z e d c o p i e s o f t h i s a r t i c l e ,

f o r w a r d

t o a n u n a u t h o r i z e d u s e r o r t o p o s t e l e c t r o n i c a l l y w



7/12


D o w

n l o a d e d f r o m w

w w . i


y A b e l G a r c i a o n 0 8 / 0 9 / 1 2 .



f o r w a r d




8/12


D o w


w w . i


y A b e l G a r c i a o n 0 8 / 0 9 / 1 2 .



f o r w a r d




9/12


D o w


w w . i


y A b e l G a r c i a o n 0 8 / 0 9 / 1 2 .



f o r w a r d




10/12


D o w


w w . i


y A b e l G a r c i a o n 0 8 / 0 9 / 1 2 .



f o r w a r d




11/12


D o w


w w . i


y A b e l G a r c i

a o n 0 8 / 0 9 / 1 2 .



f o r w a r d




12/12

kupiec paul - techniques for verifying the accuracy of risk measurement models

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