Valuing Energy Options in a One Factor Model Fitted to Forward Prices

In this paper we develop a single-factor modeling framework which is consistent with market observable forward prices and volatilities. The model is a special case of the multi-factor model developed in Clewlow and Stickland [1999b] and leads to analytical pricing formula for standard options, caps, floors, collars and swaptions. We also show how American style and exotic energy derivatives can be priced using trinomial trees, which are constructed to be consistent with the forward curve and volatility structure. We demonstrate the application of the trinomial tree to the pricing of a European and American Asian option. The analysis in this paper extends the results in Schwartz [1997] and Amin, et al. [1995].

Pricing Interest Rate Exotics in Multi-Factor Gaussian Interest Rate Models

For many interest rate exotic options, for example options on the slope of the yield curve or American featured options, a one factor assumption for term structure evolution is inappropriate. These options derive their value from changes in the slope or cuvature of the yield curve and hence are more realistically priced with multiple factor models. However, efficient construction of short rate trees becomes computationally intractable as we increase the number of factors and in particular as we move to non-Markovian models. In this paper we describe a general framework for pricing a wide range of interest rate exotic options under a very general family of multi-factor Gaussian interest rate models. Our framework is based on a computationally efficient implementation of Monte Carlo integration utilising analytical approximations as control variates. These techniques extend the analysis of Clewlow, Pang and Strickland [1997] for pricing interest rate caps and swaptions.

The Evaluation of Multiple Year Gas Sales Agreement with Regime Switching

A typical gas sales agreement (GSA) also called a gas swing contract, is an agreement between a supplier and a purchaser for the delivery of variable daily quantities of gas, between specified minimum and maximum daily limits, over a certain number of years at a specified set of contract prices. The main constraint of such an agreement that makes them difficult to value are that in each gas year there is a minimum volume of gas (termed take-or-pay or minimum bill) for which the buyer will be charged at the end of the year (or penalty date), regardless of the actual quantity of gas taken. We propose a framework for pricing such swing contracts for an underlying gas forward price curve that follows a regime-switching process in order to better capture the volatility behaviour in such markets. With the help of a recombing pentanonial tree, we are able to efficiently evaluate the prices of the swing contracts, find optimal daily decisions and optimaly early use of both the make-up bank and the carry forward bank at different regimes. We also show how the change of regime will affect the decisions.gas sales agreement; swing contract; take-or-pay; make-up; carry forward; forward price curve; regime switching volatility; recombing pentanomial tree

Modelling and Estimating the Forward Price Curve in the Energy Market

The stochastic or random nature of commodity prices plays a central role in models for valuing financial contingent claims on commodities. In this paper, by enhancing a multifactor framework which is consistent not only with the market observable forward price curve but also the volatilities and correlations of forward prices, we propose a two factor stochastic volatility model for the evolution of the gas forward curve. The volatility is stochastic due to a hidden Markov Chain that causes it to switch between "on peak" and "off peak" states. Based on the structure functional forms for the volatility, we propose and implement the Markov Chain Monte Carlo (MCMC) method to estimate the parameters of the forward curve model. Applications to simulated data indicate that the proposed algorithm is able to accommodate more general features, such as regime switching and seasonality. Applications to the market gas forward data shows that the MCMC approach provides stable estimates.

Who wins when the competition heats up? Effects of climate change on interactions among three Antarctic penguin species

This thesis sought to elucidate the mechanisms driving the large-scale population changes observed in Pygoscelis penguins in the Western Antarctic Peninsula (WAP)/Scotia Sea region since the 1970s, with particular focus on the interactions between the species. During this period the climate in this region has changed dramatically, with rapid warming and sea ice declines occurring until the late 20th century to be followed by a pause in the warming. These changes have altered biotic and abiotic conditions in the penguins’ ecosystem and researchers widely agree that this is driving their population changes. In order to elucidate the exact mechanisms of population change, we attempted to fill crucial knowledge gaps, including foraging ecology, migration and breeding success, throughout their annual cycle and all with particular focus on the interactions between the three Pygoscelis species. Direct tracking and isotope analysis provided novel insights into foraging behaviour and the role of niche partitioning between the species throughout the annual cycle, and its importance for reducing interspecific competition. During the breeding season, allochrony between Adélie and chinstrap penguins was found to reduce competitive overlap in foraging areas by 54%, compared to synchronous breeding, and to be resilient to climate change. The migration routes and over-winter sites of chinstrap penguins from the South Orkney Islands were identified for the first time and were found to be segregated from birds from the neighbouring South Shetland Islands archipelago. The environmental conditions at the two over-winter sites differed but the population trends at the two archipelagos were similar, suggesting that winter conditions are not likely to be a major driver. Developing on our findings of contrasting environmental conditions across the chinstrap over-wintering sites, we investigated the effect of multiple environmental variables on population trends in the final two thesis chapters. Sea ice has been shown to be a major driver of Adélie penguin breeding success, and thereby population trends, and birds in our study region experience particularly dramatic seasonal changes in sea ice concentration (SIC), as it is located near the northern extent of winter ice. The three Pygoscelis species are widely cited as having different ice tolerances, termed the ‘sea ice hypothesis’, with Adélies being described as ‘ice-loving’, chinstraps as ‘ice tolerant’ and gentoos as ‘ice averse’. These differing ice tolerances are thought to be a major factor in the species’ contrasting population changes in this region and these hypothesised preferences could theoretically induce a sea ice optima for breeding and forging success. However, no evidence was found for a sea ice optima at the study colony, despite previous studies finding a 20% optima for Adélies in East Antarctica, and SIC was found to have no significant effect on breeding productivity or diet composition but some effect was found for fledging mass and foraging trip duration. The combined influence of environmental conditions and interspecific interactions on the three species’ population trends was investigated for the first time in this system. Data from large and local scale climate and a long time period (more than 25 years) were investigated at the two study archipelagos using a multi-species Gompertz population model. The model failed to identify any of the modelled variables as major drivers of the population variation, suggesting that other factors, such as predation and prey availability were potentially important drivers. This thesis also identified a number of priorities for future research and identified the need for a greater emphasis on modelling the effects of Antarctic krill biomass, rather than climate variables, upon penguin demographic variables

Intersecting Sets: John Venn, Church and University, 1834-1923

This thesis is an examination of the religious and academic identities of John Venn (1834-1923), logician and biographer, explored by building up a picture of the series of family, religious and academic communities of which he was a part - from the institutional structures of the Church of England, Gonville and Caius College and the University of Cambridge, to more informal networks of friends and professions; and virtual communities of ideas and intellectual influence. Venn was heir to a clerical, Evangelical dynasty, but his religious doubts led him to resign orders. He established instead an academic reputation through published works on probability and logic; and in later life concentrated upon historical and biographical researches. Venn's departure from Evangelicalism and his development as an academic is explained in terms of the real and virtual communities he 'inherited', such as the Venn family connexion, Evangelical theology and Church party; and those to which he 'acquired' membership, namely the academic networks signified by interactions with colleagues and mediated through journals, learned societies and the institutional structures of the University. This biographical study of Venn is an entry point for examining broader historical themes in nineteenth century religion and academia; in particular, the development of mid-Victorian Evangelicalism, the course of University reform and the emergence of clerical and academic professional identities. It is also a case-study of religious doubt against which to compare the literature on crises of faith and the experiences of other sons of Evangelicalism, such as Leslie and Fitzjames Stephen and Henry Sidgwick

Cellular automata and dynamical systems

In this thesis we investigate the theoretical nature of the mathematical structures termed cellular automata. Chapter 1: Reviews the origin and history of cellular automata in order to place the current work into context. Chapter 2: Develops a cellular automata framework which contains the main aspects of cellular automata structure which have appeared in the literature. We present a scheme for specifying the cellular automata rules for this general model and present six examples of cellular automata within the model. Chapter 3: Here we develop a statistical mechanical model of cellular automata behaviour. We consider the relationship between variations within the model and their relationship to dynamical systems. We obtain results on the variance of the state changes, scaling of the cellular automata lattice, the equivalence of noise, spatial mixing of the lattice states and entropy, synchronous and asynchronous cellular automata and the equivalence of the rule probability and the time step of a discrete approximation to a dynamical system. Chapter 4: This contains an empirical comparison of cellular automata within our general framework and the statistical mechanical model. We obtain results on the transition from limit cycle to limit point behaviour as the rule probabilities are decreased. We also discuss failures of the statistical mechanical model due to failure of the assumptions behind it. Chapter 5: Here a practical application of the preceding work to population genetics is presented. We study this in the context of some established population models and show it may be most useful in the field of epidemiology. Further generalisations of the statistical mechanical and cellular automata models allow the modelling of more complex population models and mobile populations of organisms. Chapter 6: Reviews the results obtained in the context of the open questions introduced in Chapter 1. We also consider further questions this work raises and make some general comments on how these may apply to related fields

A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models

The aim of this work is to develop a simulation approach to the yield curve evolution in the Heath, Jarrow and Morton [Econometrica 60 (1) (1992) 77] framework. The stochastic quantities considered as affecting the forward rate volatility function are the spot rate and the forward rate. A decomposition of the volatility function into a Hull and White [Rev. Financial Stud. 3 (1990) 573] volatility and a remainder allows us to develop an efficient Control Variate Method that makes use of the closed form solution of the Hull and White call option. This technique considerably speeds up the simulation algorithm to approximate call option values with Monte Carlo simulation. © 2003 Elsevier B.V. All rights reserved

Disruptive Transportation: The Adoption, Utilization, and Impacts of Ride-Hailing in the United States

The rapid adoption of ride-hailing poses significant challenges for transportation researchers, policymakers, and planners, as there is limited information and data about how these services affect transportation decisions and travel patterns. Given the long-range business, policy, and planning decisions that are required to support transportation infrastructure (including public transit, roads, bike lanes, and sidewalks), there is an urgent need to collect data on the adoption of these new services, and in particular their potential impacts on travel choices. This paper presents findings from a comprehensive travel and residential survey deployed in seven major U.S. cities, in two phases from 2014 to 2016, with a targeted, representative sample of their urban and suburban populations. The purpose of this report is to provide early insight on the adoption of, use, and travel behavior impacts of ride-hailing

The Evaluation of Multiple Year Gas Sales Agreement with Regime Switching

A typical gas sales agreement (GSA), also called a gas swing contract, is an agreement between a supplier and a purchaser for the delivery of variable daily quantities of gas, between specified minimum and maximum daily limits, over a certain number of years at a specified set of contract prices. The main constraint of such an agreement that makes them difficult to value is that in each gas year there is a minimum volume of gas (termed take-or-pay or minimum bill) for which the buyer will be charged at the end of the year (or penalty date), regardless of the actual quantity of gas taken. We propose a framework for pricing such swing contracts for an underlying gas forward price curve that follows a regime-switching process in order to better capture the volatility behaviour in such markets. With the help of a recombining pentanomial tree, we are able to efficiently evaluate the prices of the swing contracts, find optimal daily decisions and optimal yearly use of both the make-up bank and the carry forward bank at different regimes. We also show how the change of regime will affect the decisions