SEMIPARAMETRIC ESTIMATION AND INFERENCE FOR CONDITIONAL VALUE-AT-RISK AND EXPECTED SHORTFALL
Open Access
- 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/Co-Advisor
Zhibiao Zhao, Committee Chair/Co-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.