A stochastic dynamic programming approach for pricing options on stock-index futures

The aim of this thesis is to price options on equity index futures with an application to standard options on S&P 500 futures traded on the Chicago Mercantile Exchange. Our methodology is based on stochastic dynamic programming, which can accommodate European as well as American options. The model accommodates dividends from the underlying asset. It also captures the optimal exercise strategy and the fair value of the option. This approach is an alternative to available numerical pricing methods such as binomial trees, finite differences, and ad-hoc numerical approximation techniques. Our numerical and empirical investigations demonstrate convergence, robustness, and efficiency. We use this methodology to value exchange-listed options. The European option premiums thus obtained are compared to Black's closed-form formula. They are accurate to four digits. The American option premiums also have a similar level of accuracy compared to premiums obtained using finite differences and binomial trees with a large number of time steps. The proposed model accounts for deterministic, seasonally varying dividend yield. In pricing futures options, we discover that what matters is the sum of the dividend yields over the life of the futures contract and not their distribution.

A Comparative Analysis of Community-Based Service Providers for "Extreme" Case ASD: Exploring Activity Program Options

The purpose of my research was to examine how community-based organizations in the Niagara region provide programs for children with Autism Spectrum Disorder (ASD), who are considered to represent “extreme” or “severe” cases. A qualitative, comparative case study was conducted that focused on three organizations who provide summer recreation and activity programs, in order to examine the issues these organizations face when determining program structure and staff training; and to understand what the threshold for physical activity is in this type of setting, and how the unique needs surrounding these “severe” cases are met while attending the program. Purposeful sampling was employed to select a supervisor and senior staff member from each organization to discuss the training process, program development and implementation, and the resources and strategies used within their organization’s community-based program. A confirming comparative analysis was comparative analysis of a parents survey with six mothers whose children are considered “severe” indicated that camp staffs’ expectations are unrealistic where as the parents and supervisors have more realistic expectations within the “real world” of camp. There is no definition of “severe” or “extreme” and therefore severity is dependent upon the context.