Monte Carlo simulation is a widely used numerical method for valuing financial derivatives. It can be used to value high-dimensional options or complex path-dependent options. Part one of the thesis is concerned with the valuation of barrier options with complex time-varying barriers. In Part one, a novel simulation method, the contour bridge method, is proposed to value exotic time-varying barrier options. The new method is applied to value several exotic barrier options, including those with quadratic and trigonometric barriers. Part two of this thesis is concerned with the valuation of American options using the Monte Carlo simulation method. Since the Monte Carlo simulation can be computationally expensive, variance reduction methods must be used in order to implement Monte Carlo simulation efficiently. Chapter 5 proposes a new control variate method, based on the use of Bermudan put options, to value standard American options. It is shown that this new control variate method achieves significant gains over previous methods. Chapter 6 focuses on the extension and the generalisation of the standard regression method for valuing American options. The proposed method, the sequential contour Monte Carlo (SCMC) method, is based on hitting time simulation to a fixed set of contours. The SCMC method values American put options without bias and achieves marginal gains over the standard method. Lastly, in Part three, the SCMC method is combined with the contour bridge method to value American knock-in options with a linear barrier. The method can value American barrier options very well and efficiency gains are observed.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:549827 |
| Date | January 2011 |
| Creators | Chirayukool, Pokpong |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/45027/ |
Page generated in 0.0016 seconds