Robust Inference with Quantile Regression in Stochastic Volatility Models withapplication to Value at Risk calculation

RQMM;SV;Quantile Regression;VaR;Indirect Inference

Saha, Paramita ; Peter Bloomfield, Committee Chair,Saha, Paramita ; Peter Bloomfield ; Committee Chair

University:North Carolina State University

关键词: RQMM;    SV;    Quantile Regression;    VaR;    Indirect Inference;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/4103/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

Stochastic Volatility (SV) models play an integral role in modeling time varyingvolatility, with widespread application in finance. Due to the absence of a closed form likelihoodfunction, estimation is a challenging problem. In the presence of outliers, and the highkurtosis prevalent in financial data, robust estimation techniques are desirable. Also, in thecontext of risk assessment when the underlying model is SV, computing the one step aheadpredictive return densities for Value at Risk (VaR) calculation entails a numerically indirectprocedure. The Quantile Regression (QR) estimation is an increasingly important tool foranalysis, which helps in fitting parsimonious models in lieu of full conditional distributions.We propose two methods (i) Regression Quantile Method of Moments (RQMM) and (ii)Regression Quantile - Kalman Filtering method (RQ-KF) based on the QR approach thatcan be used to obtain robust SV model parameter estimates as well as VaR estimates. TheRQMM is a simulation based indirect inference procedure where auxiliary recursive quantilemodels are used, with gradients of the RQ objective function providing the moment conditions.This was motivated by the Efficient Method of Moments (EMM) approach used inSV model estimation and the Conditional Autoregressive Value at Risk (CAViaR) method.An optimal linear quantile model based on the underlying SV assumption is derived. Thisis used along with other CAViaR specifications for the auxiliary models. The RQ-KF is acomputationally simplified procedure combining the QML and QR methodologies. Basedon a recursive model under the SV framework, quantile estimates are produced by theKalman filtering scheme and are further refined using the RQ objective function, yieldingrobust estimates.For illustration purposes, comparison of the RQMM method with EMM underdifferent data scenarios show that RQMM is stable under model misspecification, presenceof outliers and heavy-tailedness. Comparison of the RQ-KF method with the existing QMLmethod provide competitive results in terms of model estimation. Also, risk evaluation testresults show desirable statistical properties of the quantile estimates obtained from thesemethods. Applications to real data and simulation studies on different parameter settingsof the SV model provide empirical support in favor of the quantile model specifications.We also propose an algorithm, based on a Gram Charlier density approximationfor the conditional predictive volatility density given past returns, to compute the onestep ahead predictive return densities in the existing Nonlinear Filtering (NF) scheme.This approach is used in likelihood and VaR computations. This algorithm provides analternative approximation in the reduction of the infinite-dimensional state vector and isbased on fewer computational steps compared to the existing methods. Results based onthe algorithm are comparable to existing methods.