ABSTRACTS

Fourier Space Time-Stepping for Catastrophe Options

Valuing derivative instruments written on underliers containing jumps is a difficult task. If the jumps are driven by a Levy process, then European options can be valued using a Fourier transform technique developed by Carr & Madan; however, their method does not apply to Barrier, Bermudan or American styled contingent claims. In the past, many authors used discrete versions of the pricing partial-integro differential to value such options. In this talk I will review a novel and simple technique, based on Carr & Madan, that circumvents many problems with previous methods -- we coin our method Fourier Space Time-Stepping (FST). This method is applicable to a wide class of options, is exact between monitoring dates, easily generalizes to higher dimensions, and has a natural extension to regime switching models. I will discuss two explicit examples of Bermudan Catastrophe options.

A Tractable Stochastic Volatility Model of Forward Curve for Commodity Derivatives

For obvious reasons, it is difficult to dynamically trade commodities on the spot market. In its place, futures contracts are actively traded both for financial and physical delivery. In this talk, I will first investigate the statistical behavior of light sweet crude oil futures curves using a modification of functional data analysis. Some classical spot models and stochastic volatility generalizations will then be introduced. Finally, I will demonstrate how to model forward curves directly with stochastic volatility and outline how to value derivatives using singular perturbation theory.