This dissertation considers the pricing and hedging of contingent claims in a generalsemimartingale market. Initially the focus is on a complete market, where it ispossible to price uniquely and hedge perfectly. In this context the two fundamentaltheorems of asset pricing are explored. The...

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011.

Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be writtenin terms of the "jumps" of X are introduced, and so are discrete-data based approximations. A model selection approach made up oftwo steps is investigated. The first step...

Model selection methods and nonparametric estimation of Levy densities are presented. The estimation relies on the properties of Levy processes for small time spans, on the nature of the jumps of the process, and on methods of estimation for spatial Poisson processes. Given a linear space S of...

ENGLISH ABSTRACT: In this thesis, we propose to use Levy processes to model the dynamics of asset prices. Inthe first part, we deal with single asset options and model the log stock prices with a Levyprocess. We employ pure jump Levy processes of infinite activity, in particular variancegamma...

Recent nancial crises have highlighted the sensitivity and vulnerability of nancial marketsto ination, which reduces the value of money and a ects the net returns of nancial instruments.In response to this, investors who are concerned with maintaining their investment'spurchasing power rather...

In this paper, we introduce DSPMD, discretely sampled process with pre-specified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified marginals and pre-specified dependence. In the DSPMD for Levy processes, some regular copula can be...

In this thesis, stochastic volatility models with Levy processes are treatedin parameter calibration by the Carr-Madan fast Fourier transform (FFT) method and pricingthrough the partial integro-differential equation (PIDE) approach. First, different models where the underlying log stock price or...

The main purpose of this paper is to derive unbiased Monte Carlo estimators of various sensitivity indices for an averaged asset price dynamics governed by the gamma Lévy process. The key idea is to apply a scaling property of the gamma process with respect to the Esscher density transform...