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
SN - 0094-9655
VL - 90
SP - 1735
EP - 1752
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
IS - 10
ER -