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Abstract
In this thesis, we examine the properties that make the expectile a proper candidate for a measure of risk in finance. Expectiles are the solutions to asymmetric least squares minimization. The expectile is also closely related to two commonly used measures, value at risk and expected shortfall, which facilitates the extension of the expectile to finance. Using simulated examples, we investigate characteristics that make the expectile attractive in finance. The relationship between quantiles and expectiles is featured prominently. In addition, a method for estimating the time-varying expectile is outlined and applied to an exchange traded fund of the Dow Jones Industrial Average and the S&P 500 Stock Index.