New models for borehole valuation of new mining operations and routine valuation of ore reserve blocks

This thesis proposes some new valuation models and procedures for global and local ore reserve estimation. To obtain efficient grade and tonnage estimates for global borehole valuations of new gold mining properties, the appropriate spatial and distributional models for the mineralisation are absolutely essential. [Abbreviated Abstract. Open document to view full version]GR 201

Comparing parametric and semi-parametric approaches for bayesian cost-effectiveness analyses in health economics

We consider the problem of assessing new and existing technologies for their cost-effectiveness in the case where data on both costs and effects are available from a clinical trial, and we address it by means of the cost-effectiveness acceptability curve. The main difficulty in these analyses is that cost data usually exhibit highly skew and heavytailed distributions, so that it can be extremely difficult to produce realistic probabilistic models for the underlying population distribution, and in particular to model accurately the tail of the distribution, which is highly influential in estimating the population mean. Here, in order to integrate the uncertainty about the model into the analysis of cost data and into cost-effectiveness analyses, we consider an approach based on Bayesian model averaging: instead of choosing a single parametric model, we specify a set of plausible models for costs and estimate the mean cost with its posterior expectation, that can be obtained as a weighted mean of the posterior expectations under each model, with weights given by the posterior model probabilities. The results are compared with those obtained with a semi-parametric approach that does not require any assumption about the distribution of costs. 1 IntroductionHealthcare cost data, cost-effectiveness analysis, mixture models, Bayesian model averaging

B-spline techniques for volatility modeling

This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines obtained by including basis functions with infinite support. We first come back to the application of shape-constrained B-splines to the estimation of conditional expectations, not merely from a scatter plot but also from the given marginal distributions. An application is the Monte Carlo calibration of stochastic local volatility models by Markov projection. Then we present a new technique for the calibration of an implied volatility surface to sparse option data. We use a B-spline parameterization of the Radon-Nikodym derivative of the underlying's risk-neutral probability density with respect to a roughly calibrated base model. We show that this method provides smooth arbitrage-free implied volatility surfaces. Finally, we sketch a Galerkin method with B-spline finite elements to the solution of the partial differential equation satisfied by the Radon-Nikodym derivative.Comment: 25 page

A Non-Gaussian Option Pricing Model with Skew

Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to include volatility-stock correlations consistent with the leverage effect. A generalized Black-Scholes partial differential equation for this model is obtained, together with closed-form approximate solutions for the fair price of a European call option. In certain limits, the standard Black-Scholes model is recovered, as is the Constant Elasticity of Variance (CEV) model of Cox and Ross. Alternative methods of solution to that model are thereby also discussed. The model parameters are partially fit from empirical observations of the distribution of the underlying. The option pricing model then predicts European call prices which fit well to empirical market data over several maturities.Comment: 37 pages, 11 ps figures, minor changes, typos corrected, to appear in Quantitative Financ