Static hedging with repeated Richardson extrapolation

Abstract

This thesis explores the Repeated Richardson extrapolation technique when applied to static replication methodologies in the valuation of European-style barrier options under both the constant elasticity of variance (CEV) model and the jump to default extended constant elasticity of variance (JDCEV) model. The Richardson extrapolation is a computational tool used throughout the literature in order to improve the effciency of numerous numerical methods. In this thesis is going to be studied the benefits of its use when applied to static replication methods.

Esta tese explora a repeated Richardson extrapolation technique quando aplicada a metodologias de replicação estáticas na avaliação de opções com barreira europeias utilizando o modelo constant elasticity of variance (CEV) e o modelo jump to default extended constant elasticity of variance (JDCEV). A extrapolação de Richardson é uma ferramenta computacional usada para melhorar a eficiência de vários métodos numéricos. Nesta tese os seus benefícios vão ser explorados ao ser aplicada a métodos de replicação estática.