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.

Contract between John Cronyn and Nelson Forsyth, December 16, 1854.

John Cronyn (1827-1898) emigrated to Canada from Ireland in 1837. He studied medicine at the University of Toronto, but was not granted his degree upon completion of the requirements. He refused to take the test oaths meant to exclude Catholics from the profession and was not granted his degree until several years later, when the discriminatory laws were rescinded. In 1850, he married Elizabeth Willoughby of Toronto. They settled in Fort Erie and he established a successful medical practice there. He was active in the community, serving as Superintendent of schools and one term as Reeve. In 1859 he relocated to Buffalo and continued to practice medicine there. Cronyn was instrumental in the establishment of a medical department at Niagara University, where he was a professor and president of faculty. Nelson Forsyth was the son of William Forsyth (1771-1841), a prominent businessman in Niagara who owned and operated the Pavilion Hotel (later known as Forsyth’s Inn). Nelson was also a businessman and lived in Fort Erie with his wife Archange Warren.

Second copy of the memorandum respecting differences between the approximate and final estimate but this one has “memorandum of extras of Brown and McDonall contract” written on the outer page

Second copy of the memorandum respecting differences between the approximate and final estimate but this one has “memorandum of extras of Brown and McDonall contract” written on the outer page (3 pages, handwritten), n.d.

Memo to the warden and councilors for the County of Welland in council assembled regarding the contract of Edward Henderson

Memo to the warden and councilors for the County of Welland in council assembled regarding the contract of Edward Henderson. The terms of the contract have not been exceeded. This note is not signed, n.d.