Stochastic time-changed Lévy processes with their implementation

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.

Grantor dc:publisher.institution

Division of Actuarial Science

Year dc:date.issued

2014

Author dc:creator

• Sihlobo, Odwa

Advisor dc:contributor.advisor

• Mataramvura, Sure

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/13156

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/13156