Quantile Autoregression and its application to Financial Risk Management and Portfolio Optimization
Ananda, Omutokoh Kube
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Increasing globalization, complexity of capital markets and the expanding range of exotic financial instruments have made financial risk management difficult to evaluate. As a consequence, a rise in use of more sophisticated risk management systems has not led to better results. Most financial data exhibits time varying volatility and heavy tails therefore an appropriate risk measure should capture these features. Volatility patterns reflect different characteristics in different stock markets. The main aim of this study is to improve on volatility estimation by use of Quantile Autoregression frameworks. To avoid strong assumptions about the form of innovations, an initial proxy of volatility estimator is proposed. The estimator is assumed to capture the intraday volatility based on the conditional Interquantile Autoregressive Range. A class of a-mixing time series models based on quantile regression are used and direct estimation of coefficients as introduced by Koenker and Bassett (1978) are adopted. We study the estimation of scale function in the Quantile Autoregressive models discussed. Similar methods used to show the asymptotic properties of conditional autoregressive coefficient estimators are applied to the conditional Interquantile Autoregressive Range (IQAR) estimator and show that under some mild regularity conditions, it is consistent and asymptotically normal. A Monte Carlo study is carried out to verify theoretical properties derived for the estimator which confirms the estimator is consistent. The estimator is fitted to simulated data to show how to perform Risk management and Portfolio Optimization. An application to real data is included to illustrate Financial Risk Management and Portfolio Optimization.