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Quantitative Finance · Glosarium

Apa itu Traffic-light test?

Definition 21.16 Rates, Credit, XVA and Risk · Bab 21 — Market-Risk Measures

The traffic-light test classifies a 99% VaR model by its exceptions over 250 days: green for 0 to 4, yellow for 5 to 9 with increases of 0.40, 0.50, 0.65, 0.75 and 0.85 in the capital multiplication factor of 3, red for 10 or more (an increase of 1). Under the 1996 rules, capital is the higher of the previous day’s ten-day VaR and the factor times its average over the preceding sixty business days.

Four years of the book’s daily P&L against the negative of the previous day’s 99% VaR from historical simulation and from the EWMA delta-normal model; crosses mark the EWMA model’s exceptions. The EWMA line reacts to volatility quickly but runs too close to zero for fat-tailed days. Data: US Treasury, ECB; the chapter’s tutorial.
Figure 21.3. Four years of the book’s daily P&L against the negative of the previous day’s 99% VaR from historical simulation and from the EWMA delta-normal model; crosses mark the EWMA model’s exceptions. The EWMA line reacts to volatility quickly but runs too close to zero for fat-tailed days. Data: US Treasury, ECB; the chapter’s tutorial.

Contoh

Example 21.17 (Four years of backtesting)

Recomputing each model every day from 2 September 2022 to 23 September 2026, on the same book revalued at each day’s levels, against the next day’s P&L: historical simulation has 10 exceptions in 1 000 days (Kupiec p-value 1.00) and none in the last 250, green; the EWMA delta-normal model has 28 (Kupiec likelihood ratio 22.0, p-value 3×10−63\times10^{-6}) and 8 in the last 250, yellow with a 0.75 increase; filtered historical simulation has 8 and 3, green (Figure 21.3). None fails the independence test at 5%.

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