Document Type

Theses, Ph.D


Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence


5.2 ECONOMICS AND BUSINESS, Business and Management., Econometrics

Publication Details

Thesis Submitted for the Award of PhD (Doctor of Philosophy)


Options play an important role in the financial world and are actively traded with huge trading volume. Most of the options traded on exchanges are American options. Spanning over a few decades, the American option pricing problem continues to intrigue scholars and practitioners in finance. The employee stock options (ESOs), a variant of American options, has been increasingly popular for firms to compensate, motivate and retain employees. ESOs importantly do not trade in markets nevertheless fair value must be determined – often by accountants. Unique features of ESOs however complicate the valuation. Our research, consisting of three papers, focuses on the improved lattice techniques for valuing American options and ESOs. Research paper 1 (Chapter 2) introduces an intelligent lattice search algorithm to efficiently locate the optimal exercise boundary for American options. The computational runtime can be reduced from over 18 minutes down to less than 3 seconds to estimate a 15,000-step CRR binomial tree. Research paper 2 (Chapter 3) introduces a set of lattice techniques to the Leisen-Reimer and Tian binomial models for American options pricing. A level of accuracy and efficiency combined can be achieve that surpass analytical solution models prominent in the literature. Moreover, lattices importantly afford an explicit trade-off locus between accuracy and speed that can be navigated according to predetermined precision tolerance levels and option types. These should have practical relevance to trading platforms that require real-time estimates of implied volatility. Research paper 3 (Chapter 4) proposes adjustments to the Hull-White ESO pricing model, based on insights developed by Boyle-Lau and Tian specifications. The proposed Hull-White-Boyle-Lau and Hull White-Tian revamps expand the practicable menu choice available to stakeholders tasked with the valuation of these ESOs. Accountants, across many jurisdictions, are subjected to higher demands for disclosure and fair valuation. The streamlined valuation approaches developed here may prove ii useful in expanding the tool kit of practicable/workable models. This improved efficiency can be harnessed even at the level of a basic spreadsheet and this this should assist in testing, validating and benchmarking valuation in lattices and in evaluating the newer generation of closed-form solutions emerging in the literature.