Esben Høg

On the Generalized Brownian Motion and its Applications in Finance

This paper deals with dynamic term structure models (DTSMs) and proposes a new way to handle the limitation of the classical affine models. In particular, the paper expands the exibility of the DTSMs by applying generalized Brownian motions with dependent increments as the governing force of the state variables instead of standard Brownian motions. This is a new direction in pricing non defaultable bonds. By extending the theory developed by Dippon & Schiemert (2006a), the paper developes a bond market with memory, and proves the absence of arbitrage. The framework is readily extendable to other markets or multi factors. As a complement the paper shows an example of how to derive the implied bond pricing parameters using the ordinary Kalman filter.

Non-Parametric Estimation of Diffusion-Paths Using Wavelet Scaling Methods

Abstract In continuous time, diffusion processes have been used to model financial dynamics for a long time. For example the Ornstein-Uhlenbeck process (the simplest mean-reverting process) has been used to model non-speculative price processes. We discuss non-parametric estimation of these processes using a wavelet filtration method, specifically the a trous algorithm.