SEMIPARAMETRIC ESTIMATION AND INFERENCE FOR CONDITIONAL VALUE-AT-RISK AND EXPECTED SHORTFALL

Restricted (Penn State Only)
Author:
Wang, Chuan-Sheng
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
February 26, 2018
Committee Members:
  • Zhibiao Zhao, Dissertation Advisor
  • Zhibiao Zhao, Committee Chair
  • Runze Li, Committee Member
  • Lingzhou Xue, Committee Member
  • Fuqing Zhang, Outside Member
Keywords:
  • Bootstrap
  • Conditional expected shortfall
  • Conditional Value-at-Risk
  • Nonlinear time series
  • Quantile regression
  • Semiparametric methods
Abstract:
Conditional Value-at-Risk (hereafter, CVaR) and Expected Shortfall (CES) play an important role in financial risk management. Parametric CVaR and CES enjoy both nice interpretation and capability of multi-dimensional modeling, however they are subject to errors from mis-specification of the noise distribution. On the other hand, nonparametric estimations are robust but suffer from the ''curse of dimensionality'' and slow convergence rate. To overcome these issues, we study semiparametric CVaR and CES estimation and inference for parametric model with nonparametric noise distribution. In this dissertation, under a general framework that allows for many widely used time series models, we propose a semiparametric CVaR estimator and a semiparametric CES estimator that both achieve the parametric convergence rate. Asymptotic properties of the estimators are provided to support the inference. Furthermore, to draw simultaneous inference for CVaR at multiple confidence levels, we establish a functional central limit theorem for CVaR process indexed by the confidence level and use it to study the conditional expected shortfall. A user-friendly bootstrap approach is introduced to facilitate non-expert practitioners to perform confidence interval construction for CVaR and CES. The methodology is illustrated through both Monte Carlo studies and an application to S&P 500 index.