Semiparametric Estimation of Value-at-Risk 1

Value at Risk is a fundamental tool for managing market risks. It measures the worst loss to be expected of a portfolio over a given time horizon under normal market conditions at a given confidence level. Calculation of VaR frequently involves estimating the volatility of return processes and quantiles of standardized returns. In this paper, several semiparametric techniques are introduced to estimate the volatilities of the market prices of a portfolio. In addition, both parametric and nonparametric techniques are proposed to estimate the quantiles of standardized return processes. The newly proposed techniques also have the flexibility to adapt automatically to the changes in the dynamics of market prices over time. Their statistical efficiencies are studied both theoretically and empirically. The combination of newly proposed techniques for estimating volatility and standardized quantiles yields several new techniques for forecasting multiple period VaR. The performance of the newly proposed VaR estimators is evaluated and compared with some of existing methods. Our simulation results and empirical studies endorse the newly proposed time-dependent semiparametric approach for estimating VaR.

[1]  Jianqing Fan,et al.  Time-dependent Diffusion Models for Term Structure Dynamics and the Stock Price Volatility , 2003 .

[2]  Jianqing Fan,et al.  A Reexamination of Diffusion Estimators With Applications to Financial Model Validation , 2003 .

[3]  Mike K. P. So,et al.  On conditional moments of garch models, with applications to multiple period value at risk estimation , 2003 .

[4]  N. Shephard,et al.  Econometric analysis of realized volatility and its use in estimating stochastic volatility models , 2002 .

[5]  J. Corcoran.  Modelling Extremal Events for Insurance and Finance , 2002 .

[6]  N. Shephard,et al.  Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics , 2001 .

[7]  Stephen Gray,et al.  Semiparametric ARCH models , 2001 .

[8]  Helmut Herwartz,et al.  Time Inhomogeneous Multiple Volatility Modeling , 2003 .

[9]  A. Lo,et al.  Nonparametric Risk Management and Implied Risk Aversion , 2000 .

[10]  Phhilippe Jorion.  Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[11]  Jon Danielsson,et al.  Value-at-Risk and Extreme Returns , 2000 .

[12]  Andrea Beltratti,et al.  Computing value at risk with high frequency data , 1999 .

[13]  Thierry Jeantheau,et al.  Parameter estimation for discretely observed stochastic volatility models , 1999 .

[14]  Jens Perch Nielsen,et al.  Nonparametric Autoregression with Multiplicative Volatility and Additive mean , 1999 .

[15]  Neil D. Pearson,et al.  Is the Short Rate Drift Actually Nonlinear , 2000 .

[16]  S. Aiguo,et al.  Evolving Gaussian RBF network for nonlinear time series modelling and prediction , 1998 .

[17]  Kevin Dowd,et al.  Beyond Value at Risk: The New Science of Risk Management , 1998 .

[18]  Andre Lucas,et al.  A Note on Optimal Estimation From a Risk-Management Perspective Under Possibly Misspecified Tail Behavior , 2000 .

[19]  Gerhard Stahl,et al.  On the Accuracy of VAR Estimates Based on the Variance-Covariance Approach , 1997 .

[20]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[21]  W. Perraudin,et al.  Bank Capital and Value at Risk , 1997 .

[22]  D. Hendricks,et al.  Evaluation of Value-at-Risk Models Using Historical Data , 1996 .

[23]  Til Schuermann,et al.  Converting 1-Day Volatility to h-Day Volatility : Scaling by is Worse than You Think , 1996 .

[24]  Robert F. Engle,et al.  ARCH: Selected Readings , 1995 .

[25]  Tanya Styblo Beder,et al.  VAR: Seductive but Dangerous , 1995 .

[26]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[27]  Campbell R. Harvey,et al.  An Empirical Comparison of Alternative Models of the Short-Term Interest Rate , 1992 .

[28]  J. Wooldridge,et al.  Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances , 1992 .

[29]  F. Black,et al.  Bond and Option Pricing when Short Rates are Lognormal , 1991 .

[30]  Alan G. White,et al.  Pricing Interest-Rate-Derivative Securities , 1990 .

[31]  F. Black,et al.  A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options , 1990 .

[32]  M. Crowder,et al.  Asymptotic theory of statistical inference , 1987 .

[33]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .