Stochastic time-changed Lévy processes with their implementation

Sihlobo, Odwa

Stochastic time-changed Lévy processes with their implementation

Master Thesis

2014

Publisher

University of Cape Town

Department

Division of Actuarial Science

Faculty

Faculty of Commerce

Abstract

We focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters.

Description

Includes bibliographical references.

Keywords

Financial Mathematics

Reference:

Collections

Masters

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