Estimation of Market Risk Volatility Using Interquantile Autoregressive Range

Abstract

Volatility is a market risk measure. It plays a central role in asset/derivative pricing, asset allocation/ portfolio creation, and in financial risk management. Volatility in financial applications is usually estimated using standard deviation for a given time series data. The stylized facts of financial time series data have made usage of standard deviation as an estimate for volatility, inappropriate. In order to address this problem we use the robust quantile regression procedure in estimation and also to capture the dynamic nature of volatility. In the thesis, an objective function was formulated and the function properties were investigated. The function was used to estimate quantile autoregression functions by minimization method. Volatility was then obtained by dividing the interquantile autoregression range function with a constant scale in a known distribution. The conditional quantile autoregression function is consistent and asymptotically normal. By Slutsky’s Theorem, the volatility estimator was found to be consistent. A simulation study carried out also showed that the estimator was consistent. The InterQuantile Autoregressive Range method was applied to Real data to estimate the market risk volatility of Kenyan Securities Market.