(
A) I have used right-tail analysis in all SHORT models.
(B)
Value-at-Risk
In addition
to having calculated
the academic coverage tests:
- (i) Kupiec (unconditional coverage)
- (ii) Christoffersen (conditional coverage)
there is
the industry standard "Zone" or traffic light system, for VaR, as described in:
"Basel Committee on Banking Supervision, Supervisory Framework for
the Use of 'Backtesting' in Conjunction with
the Internal Models Approach
to Market Risk Capital Requirements", January, 1996.
https://www.bis.org/publ/bcbs22.htm
In RATS, there is no CDF binomial distribution function, and as I may be using different parameter values for N and p,
to replicate Table 2 (in
the above which has N=250, p=0.01), I have used
the Normal approximation
to the binomial with continuity correction 0.5.
Code: Select all
comp N = 250; * 500, 750, 1000, 1250, 1500, 1750, 2000
comp p = 0.01; * 0.025, 0.05
* The Normal approximation to the Binomial (asymptotic Normal distribution) is used
* to compute the Cumulative Probabilities
comp mu = (N * p)
comp sigma = sqrt( N * p * (1-p) )
comp xx=%seqa(0.5,1.0,11); * continuity correction 0.5
disp xx
dec vect f(%size(xx))
ewise f(j)=%cdf((xx(j)-mu)/sigma)
disp f
But, those cumulative probabilities are not exact as in Table 2. How do I calculate exact values, or does
the Normal approximation suffice including continuity correction?
In my results I want
to add an additional column 'Basel Zone Approach
to VaR' with entries Green, Yellow, Red; based on
the total number of breaches/triggers in
the LAST rolling backtest OOS period, for EACH multi-step ahead forecast e.g. for h=1 step, for h=2 step, for h=3 step, etc
Although, on initial readings,
the "Zone" system is not as 'powerful' as
the academic coverage tests e.g. there can be rejections of
the null
- (i) VaR model correctly specified
- (ii) independence
for violation ratios > 0
whereas
the "Zone" system says
a total violation = 0
to 4, (N=250, p=0.01) is acceptable of
a Green model.
The "Zones" defined as:
Green if PHI(z) < 0.95;
Yellow if 0.95 ≤ PHI(z) < 0.9999;
Red if PHI(z) ≥ 0.9999.
Expected Shortfall
I'd also like
to do similar for ES as in
the following:
COSTANZINO N and CURRAN M (2018)
A simple traffic light approach
to backtesting expected shortfall, Risks, 6(1), 2
An earlier version:
https://papers.ssrn.com/sol3/papers.cfm ... id=2603976
I want
to generate (ideally exact, but that's complicated and involves root-finding) numbers as in Table 2, N=250, p=0.025, again using Normal approximation
to the binomial, based on equation (3.13) in
the paper,
comp mu = (0.5 * N * p)
comp sigma = sqrt( N * p * ( (4 - (3 * p))/12 ) )
etc
Does that seem reasonable?
), fixed-window rolling backtests, and judging VaR's w.r.t. violation ratios, LONG's are superior 