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Robust Volatility Estimation and Analysis of the Leverage Effect

Using volatility estimation as the underlying commonality this thesis traverses the statistical problem of robust estimation of scale, through to the financial problem of valuing call options over stock. We use a large simulation study of robust scale estimators to benchmark a nonparametric volatility estimation procedure, which not only uses techniques which are particularly suited to observed financial returns, but also addresses the problem of bias in any robust volatility estimation procedure. Existing option pricing models are discussed with careful study of the assumed volatility and elasticity of volatility with respect to stock price relationships for each of these models. An option pricing formula is derived which extends existing methods, and provides a closed form solution which can be readily computed. Preliminary analysis of real price data suggests this model is able to explain observed leverage phenomena.