This thesis comprises of five chapters. The first chapter gives a brief introduction on the Black-Scholes model and the Heston model that are used to develop a valuation framework for the European-style options. The numerical techniques that are applied to price the options-the fast Fourier transform (FFT) and the Monte Carlo simulation, are also introduced. The second chapter extends the existent literature on the pricing of power options. Under the Black-Scholes model and the Heston model, the equations for the characteristic functions for power options are solved, which are essential to effectively implement the FFT technique. In addition, under the Black-Scholes model, the Greeks for the power options, a power put-power call parity relationship, and a transformation relationship between vanilla options and power options are derived. Numerical experiments are run to evaluate the performance of the FFT approach. The results are compared to the approximations obtained from the Monte Carlo simulation. The third chapter extends the existent literature on the valuation of extendible options. The characteristic functions for extendible options are derived, under the Black-Scholes model and the Heston model, by separating the expectations into different segments. This chapter shows that the characteristic function for a one-time extendible option consists of a one-variate and a two-variate characteristic functions; hence this leads to a one-dimensional and a two-dimensional FFT application. Numerical experiments are run for an evaluation of the performance of the FFI. and the results are compared with the valuations obtained from the Monte Carlo simulation. The fourth chapter extends the second chapter by introducing a barrier feature to the power option. This is a combination of a power option and a barrier option which is named the power barrier opt ion. The closed-form solution is derived under the Black-Scholes model using the risk-neutral valuation approach. The final chapter gives the summaries of chapter two, three and four with suggestions for further development on the work in this thesis.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:605554 |
| Date | January 2013 |
| Creators | Ibrahim, Siti Nur Iqmal |
| Publisher | University of Essex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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