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...

Daily average temperature variations are modelled with a mean-reverting Ornstein-Uhlenbeck process driven by a generalized hyperbolic Levy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite...

Arbitrage theory is used to price forward (futures) contracts in energy markets, where the underlying assets are non-tradeable. The method is based on the so-called 'fitting of the yield curve' technique from interest rate theory. The spot price dynamics of Schwartz is generalized to...

Following the increasing awareness of the risk from volatility fluctuations, the market for hedging contracts written on realized volatility has surged. Companies looking for means to secure against unexpected accumulation of market activity can find over-the-counter products written on...

In this note, we prove that under some minor conditions on $\sigma$, if a martingale $X_t = \int_0^t \sigma_u dW_u $ satisfies, for every given pair $u \geq 0, \, \xi \geq 0$, $X_{u+\xi}-X_u{\mathop{=}^{\mathrm{(law)}}} X_{\xi},$ then necessarily, $|\sigma_u|$ is a constant and X is a constant...

We analyse the equilibrium asset pricing implications for an economy with single period return exposures to explicit non-Gaussian systematic factors, that may be both skewed and long-tailed, and Gaussian idiosyncratic components. Investors maximize expected exponential utility and equilibrium...