TY - JOUR

T1 - Reduced-bias and partially reduced-bias mean-of-order-p value-at-risk estimation: a Monte-Carlo comparison and an application

AU - Gomes, M. Ivette

AU - Caeiro, Frederico

AU - Figueiredo, Fernanda

AU - Henriques-Rodrigues, Lígia

AU - Pestana, Dinis

N1 - UID/MAT/0006/2019
UIDB/0006/2020
UID/MAT/0297/2019
UIDB/0297/2020

PY - 2020/7/2

Y1 - 2020/7/2

N2 - On the basis of a sample of either independent, identically distributed or possibly weakly dependent and stationary random variables from an unknown model F with a heavy right-tail function, and for any small level q, the value-at-risk (VaR) at the level q, i.e. the size of the loss that occurs with a probability q, is estimated by new semi-parametric reduced-bias procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p an adequate real number. After a brief reference to the asymptotic properties of these new VaR-estimators, we proceed to an overall comparison of alternative VaR-estimators, for finite samples, through large-scale Monte-Carlo simulation techniques. Possible algorithms for an adaptive VaR-estimation, an application to financial data and concluding remarks are also provided.

AB - On the basis of a sample of either independent, identically distributed or possibly weakly dependent and stationary random variables from an unknown model F with a heavy right-tail function, and for any small level q, the value-at-risk (VaR) at the level q, i.e. the size of the loss that occurs with a probability q, is estimated by new semi-parametric reduced-bias procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p an adequate real number. After a brief reference to the asymptotic properties of these new VaR-estimators, we proceed to an overall comparison of alternative VaR-estimators, for finite samples, through large-scale Monte-Carlo simulation techniques. Possible algorithms for an adaptive VaR-estimation, an application to financial data and concluding remarks are also provided.

KW - Bias reduction

KW - heavy right-tails

KW - heuristic methods

KW - Monte-Carlo simulation

KW - Primary 62G32

KW - Secondary 65C05

KW - semi-parametric estimation

KW - statistics of extremes

KW - value-at-risk estimation

UR - http://www.scopus.com/inward/record.url?scp=85082605252&partnerID=8YFLogxK

U2 - 10.1080/00949655.2020.1746787

DO - 10.1080/00949655.2020.1746787

M3 - Article

AN - SCOPUS:85082605252

VL - 90

SP - 1735

EP - 1752

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

IS - 10

ER -