Problem
Research questions and friction points this paper is trying to address.
e-backtesting
expected shortfall
sample size determination
value-at-risk
On E-Backtesting: Generalizations and Sample Size Determination
๐ค AI Summary
ๆฌๆๆๅบไบไธ็ง็กฎๅฎๆ ทๆฌ้็ๆนๆณ๏ผไปฅๆฃๆต้ขๆไธ่ถณ้ฎ้ข๏ผ้่ฟๅฉ็จe-็ป่ฎก้็ปๆๅไผฏๅชๅฉ้ๆบๅ้ๅบๅๆฅๆจๅฏผๆ้ๆ ทๆฌ้็ไธ็ใ
๐ Abstract
We present an approach for determining sample sizes required to detect underestimations of the expected shortfall with a prescribed power when applying the recently proposed e-backtesting procedure. We consider scenarios in which the value-at-risk at level $p$ is always estimated correctly, while the difference between the true expected shortfall and the value-at-risk is underestimated by a given factor $r$. We show that exploiting the structure of the backtest e-statistic proposed for backtesting the expected shortfall at level $p$ enables the derivation of approximate lower bounds for the required sample sizes by considering a sequence of independent and identically distributed Bernoulli random variables. We also discuss potential limitations of this approximation and compare the resulting sample size requirements with those obtained in practical applications using Monte Carlo simulations. Furthermore, we present generalizations of the e-backtesting procedure, in particular to risk measures which constitute Bayes pairs.
Innovation
Methods, ideas, or system contributions that make the work stand out.
e-backtesting
expected shortfall
sample size determination
Bayes pairs
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