Lookback option is a well-known path-dependent option where its payoff depends on the historical extremum prices. The thesis focuses on the binomial pricing of the American floating strike lookback put options with payoff at time $t$ (if exercise) characterized by \[ \max_{k=0, \ldots, t} S_k - S_t, \] where $S_t$ denotes the price of the underlying stock at time $t$. Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and Vorst} (RBCV, 1992) who proposed a transformed binomial lattice model for efficient pricing of this class of option, this thesis extends and enhances their binomial recursive algorithm by exploiting the additional combinatorial properties of the lattice structure. The proposed algorithm is not only computational efficient but it also significantly reduces the memory constraint. As a result, the proposed algorithm is more than 1000 times faster than the original RBCV algorithm and it can compute a binomial lattice with one million time steps in less than two seconds. This algorithm enables us to extrapolate the limiting (American) option value up to 4 or 5 decimal accuracy in real time.

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Lookback option is a well-known path-dependent option where its payoff depends on the historical extremum prices. The thesis focuses on the binomial pricing of the American floating strike lookback put options with payoff at time $t$ (if exercise) characterized by \[ \max_{k=0, \ldots, t} S_k - S_t, \] where $S_t$ denotes the price of the underlying stock at time $t$. Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and Vorst} (RBCV, 1992) who proposed a transformed binomial lattice model for efficient pricing of this class of option, this thesis extends and enhances their binomial recursive algorithm by exploiting the additional combinatorial properties of the lattice structure. The proposed algorithm is not only computational efficient but it also significantly reduces the memory constraint. As a result, the proposed algorithm is more than 1000 times faster than the original RBCV algorithm and it can compute a binomial lattice with one million time steps in less than two seconds. This algorithm enables us to extrapolate the limiting (American) option value up to 4 or 5 decimal accuracy in real time.

There are experimental based software packages as well as traffic simulation models that are used for analyzing life cycle cost of road projects. Among those our study was focused on currently available models to analyze the road user delay costs and to identify factors affecting road user delay costs. Sensitivity analyses were performed to identify the important factors that influence the user delay cost. Finally, prediction of future traffic demand as well as user delay cost, using the binomial lattice model, were presented to include the uncertainty of future traffic and user delay costs. The results of this study could help the highway designers with evaluating the future traffic.

Contemporary research indicates that the era of autonomous vehicles (AVs) is not only inevitable but may be reached sooner than expected; however, not enough research has been done to address road infrastructure readiness for supporting AV operations. Highway agencies at all levels of governments seek to identify the needed infrastructure changes to facilitate the successful integration of AVs into the existing roadway system. Given multiple sources of uncertainty particularly the market penetration of AVs, agencies find it difficult to justify the substantial investments needed to make these infrastructure changes using traditional value engineering approaches. It is needed to account for these uncertainties by doing a phased retrofitting of road infrastructure to keep up with the AV market penetration. This way, the agency can expand, defer, or scale back the investments at a future time. This dissertation develops a real options analysis (ROA) framework to address these issues while capturing the monetary value of investment timing flexibility. Using key stakeholder feedback, an extensive literature review, and discussions with experts, the needed AV-motivated changes in road infrastructure were identified across two stages of AV operations; the transition phase and the fully-autonomous phase. For a project-level case study of a 66-mile stretch of Indiana’s four-six lane Interstate corridor, two potential scenarios of infrastructure retrofitting were established and evaluated using the net present value (NPV) and ROA approaches. The results show that the NPV approach can lead to decisions at the start of the evaluation period but does not address the uncertainty associated with AV market penetration. In contrast, ROA was found to address uncertainty by incorporating investment timing flexibility and capturing its monetary value. Using the dissertation’s framework, agencies can identify and analyze a wide range of possible scenarios of AV-oriented infrastructure retrofitting to enhance readiness, at both the project and network levels.

Reservoir economic performance is based upon future cash flows which can be generated from a reservoir. Future cash flows are a function of hydrocarbon volumetric flow rates which a reservoir can produce, and the market conditions. Both of these functions of future cash flows are associated with uncertainties. There is uncertainty associated in estimates of future hydrocarbon flow rates due to uncertainty in geological model, limited availability and type of data, and the complexities involved in the reservoir modeling process. The second source of uncertainty associated with future cash flows come from changing oil prices, rate of return etc., which are all functions of market dynamics. Robust integration of these two sources of uncertainty, i.e. future hydrocarbon flow rates and market dynamics, in a model to predict cash flows from a reservoir is an essential part of risk assessment, but a difficult task. Current practices to assess a reservoir’s economic performance by using Deterministic Cash Flow (DCF) methods have been unsuccessful in their predictions because of lack in parametric capability to robustly and completely incorporate these both types of uncertainties. This thesis presents a procedure which accounts for uncertainty in hydrocarbon production forecasts due to incomplete geologic information, and a novel real options methodology to assess the project economics for upstream petroleum industry. The modeling approach entails determining future hydrocarbon production rates due to incomplete geologic information with and without secondary information. The price of hydrocarbons is modeled separately, and the costs to produce them are determined based on market dynamics. A real options methodology is used to assess the effective cash flows from the reservoir, and hence, to determine the project economics. This methodology associates realistic probabilities, which are quantified using the method’s parameters, with benefits and costs. The results from this methodology are compared against the results from DCF methodology to examine if the real options methodology can identify some hidden potential of a reservoir’s performance which DCF might not be able to uncover. This methodology is then applied to various case studies and strategies for planning and decision making. / text