This paper presents closed-form expressions for pricing Bermudan options in terms of an infinite series of standard solutions of the Black-Scholes equation. These standard solutions are combined for successive exercise dates using backward induction. At each exercise date, the optimal exercise...

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...

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...

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

We define the class of local Lévy processes. These are Lévy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded...

Deposit Guarantee Schemes (DGSs) are institutions whose main aim is to provide a safety net for depositors. If a bank fails, depositors will recover their bank deposits up to a certain limit. During the recent financial crisis, DGSs were brought at the centre of the political and financial...

We analyze the specifications of option pricing models based on time- changed Levy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process...