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from the profession and was not granted his degree until several years later, when the discriminatory laws were rescinded.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.

Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models

Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction. My master thesis research focuses on designing accelerated life testing experiments for reliability estimation. We consider multiple step-stress ALT plans with censoring. The optimal stress levels and times of changing the stress levels are investigated. We discuss the optimal designs under three optimality criteria. They are D-, A- and Q-optimal designs. We note that the classical designs are optimal only if the model assumed is correct. Due to the nature of prediction made from ALT experimental data, attained under the stress levels higher than the normal condition, extrapolation is encountered. In such case, the assumed model cannot be tested. Therefore, for possible imprecision in the assumed PH model, the method of construction for robust designs is also explored.

Contract signed by Robert Duffin of Grantham Township

Contract signed by Robert Duffin of the Township of Grantham Labourers to break stone for the proposed road from Queenston to St. Davids, 1838.

Memorandum of material furnished for superstructure on the line of the Port Dalhousie Thorold Railway by contract

Memorandum of material furnished for superstructure on the line of the Port Dalhousie Thorold Railway by contract. This document includes: Bills of timber, memorandums of planking, fencing, ties, track laying, masonry and bolts and spikes. There are also diagrams of culverts. One of the pages is loose and the outer pages are somewhat discoloured (32 pages, handwritten and bound with ribbon, n.d.

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.

The law and economics of good faith in the civil law of contract

Good faith plays a central role in most legal systems, yet appears to be an intractable concept. This article proposes to analyse it economically as the absence of opportunism in circumstances which lend themselves to it. One of the objectives underlying the law of contract on an economic view is to curtail opportunism. In spelling out what this means, the paper proposes a three-step test: bad faith is present where a substantial informational or other asymmetry exists between the parties, which one of them turns into an undue advantage, considered against the gains both parties could normally expect to realise through the contract, and where loss to the disadvantaged party is so serious as to provoke recourse to expensive self-protection, which significantly raises transactions costs in the market. The three-step test is then used to analyse a set of recent decisions in international commercial transactions and three concepts derived from good faith: fraud, warranty for latent defects and lesion.

Wage Flexibility and Contract Structure in Germany

In this paper, we look at how labor market conditions at different points during the tenure of individuals with firms are correlated with current earnings. Using data on individuals from the German Socioeconomic Panel for the 1985-1994 period, we find that both the contemporaneous unemployment rate and prior values of the unemployment rate are significantly correlated with current earnings, contrary to results for the American labor market. Estimated elasticities vary between 9 and 15 percent for the elasticity of earnings with respect to current unemployment rates, and between 6 and 10 percent with respect to unemployment rates at the start of current firm tenure. Moreover, whereas local unemployment rates determine levels of earnings, national rates influence contemporaneous variations in earnings. We interpret this result as evidence that German unions do, in fact, bargain over wages and employment, but that models of individualistic contracts, such as the implicit contract model, may explain some of the observed wage drift and longer-term wage movements reasonably well. Furthermore, we explore the heterogeneity of contracts over a variety of worker and job characteristics. In particular, we find evidence that contracts differ across firm size and worker type. Workers of large firms are remarkably more insulated from the job market than workers for any other type of firm, indicating the importance of internal job markets.

The Alberta Dilemma: Optimal Sharing of a Water Resource by an Agricultural and an Oil Sector

The purpose of this paper is to characterize the optimal time paths of production and water usage by an agricultural and an oil sector that have to share a limited water resource. We show that for any given water stock, if the oil stock is sufficiently large, it will become optimal to have a phase during which the agricultural sector is inactive. This may mean having an initial phase during which the two sectors are active, then a phase during which the water is reserved for the oil sector and the agricultural sector is inactive, followed by a phase during which both sectors are active again. The agricultural sector will always be active in the end as the oil stock is depleted and the demand for water from the oil sector decreases. In the case where agriculture is not constrained by the given natural inflow of water once there is no more oil, we show that oil extraction will always end with a phase during which oil production follows a pure Hotelling path, with the implicit price of oil net of extraction cost growing at the rate of interest. If the natural inflow of water does constitute a constraint for agriculture, then oil production never follows a pure Hotelling path, because its full marginal cost must always reflect not only the imputed rent on the finite oil stock, but also the positive opportunity cost of water.