The present thesis provides a definite answer to the question of how comparisons of certain aggregate quantities and price levels should be made across two or more geographic regions. It does so from the viewpoint of both economic theory and the “test” (or “axiomatic”) approach to index-number theory. Chapter 1 gives an overview of the problem of multilateral interspatial comparisons and introduces the rest of the thesis. Chapter 2 focuses on a particular domain of comparison involving consumer goods and services, countries and households in developing a theory of international comparisons in terms of the the (Kontis-type) cost-of-living index. To this end, two new classes of purchasing power parity measures are set out and the relationship between them is explored. The first is the many-household analogue of the (single-household) cost-of-living index and, as such, is rooted in the theory of group cost-of-living indexes. The second Consists of sets of (nominal) expenditure-share deflators, each corresponding to a system of (real) consumption shares for a group of countries. Using this framework, a rigorous exact index- number interpretation for Diewert’s “own-share” system of multilateral quantity indexes is provided. Chapter 3 develops a novel multilateral test approach to the problem at hand by generalizing Eichhorn and Voeller’s bilateral counterpart in a sensible manner. The equivalence of this approach to an extended version of Diewert’s multilateral test approach is exploited in an assessment of the relative merits of several alternative multilateral comparison formulae motivated outside the test-approach framework. Chapter 4 undertakes an empirical comparison of the formulae examined on theoretical grounds in Chapter 3 using an appropriate cross-sectional data set constructed by the Eurostat—OECD Purchasing Power Parity Programme. The principal aim of this comparison is to ascertain the magnitude of the effect of choosing one formula over another. In aid of this, a new indicator is proposed which facilitates the measurement of the difference between two sets of purchasing power parities, each computed using a different multilateral index-number formula. / Arts, Faculty of / Vancouver School of Economics / Graduate

We present a tree algorithm, called the willow tree, for financial derivative pricing. The setup of the tree uses a fixed number of spatial nodes at each time step. The transition probabilities are determine by solving linear programming problems. The willow tree method is radically superior in numerical performance when compared to the binomial tree method. / Science, Faculty of / Mathematics, Department of / Graduate

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Stocks and similar securities are normally traded in prices which are integral multiples of one-eiqhth of a dollar (a few are traded in one-sixteenths of a dollar). This price constraint may introduce a bias in the estimates of beta for low-priced securities, and the purpose of this dissertation is to examine the bias introduced from this source. The research methodology briefly consists of constructing a price series for a hypothetical stock by computing"true" prices from an assumed"true" beta and alpha, the series of returns generated from a market index, and a random disturbance term. The constructed price series is rounded to the nearest one-eighth of a dollar and an"observed" beta for this rounded price series is calculated. The"observed” beta is compared to the"true" beta to observe the degree of bias. Replications are made which differ in their randomly chosen starting point in the market index series; and the experiment is repeated for various"true" betas and alphas within the range of interest, for different intervals between price observations, and for different initial prices. Chapter I provides an introduction to the study. In Chapter II the relevant literature for this study is reviewed. The first part includes previous studies of the one-eighth effect and the intervalling effect, while the second part of the chapter focuses on the composition and characteristics of common market indexes. The analytical considerations are discussed in Chapter III. The price generating mechanism and the constraint placed upon it by one eighth price rounding are explicitly stated. Alternative rounding procedures are presented and their implications discussed. In the next section the characteristics of the rounding functions are discussed. Finally, expressions for the amount of bias in beta estimates introduced by the one eighth price rounding are derived for both logarithmic returns and holding period (arithmetic) returns. In Chapter IV the methodology used to secure the results presented in Chapter V is reviewed. The simulation itself is discussed as well as the statistical and ad hoc procedures used to evaluate the results. The results presented in the next chapter also include the results pertinent to two ancillary issues discussed in Chapter IV, namely, how many replications are needed and how reproducible are the results. Chapter VI summarizes the findings, draws a conclusion, and suggests extensions of the study. / Ph. D.

Cheng Wing Yan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 115-122). / Abstracts in English and Chinese. / Abstract --- p.i-ii / Acknowledgements --- p.iii / Table of Contents --- p.iv / List of Tables --- p.v / List of Figures --- p.vi-vii / List of Charts --- p.viii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Literature Review --- p.4 / Chapter Chapter 3. --- Methodology --- p.8 / Chapter Chapter 4. --- Data Description --- p.18 / Chapter Chapter 5. --- Empirical Results --- p.29 / Chapter 5.1 --- Simple Regression Results --- p.29 / Chapter 5.2 --- Structural Break Test Results --- p.31 / Chapter 5.3 --- Regression Results for Housing Attributes' Coefficients on Macroeconomic Variables --- p.32 / Chapter Chapter 6. --- Conclusion --- p.34 / Appendix 1. Limitation --- p.35 / Appendix 2. Tables --- p.37 / Appendix 3. Figures --- p.77 / Appendix 4. Charts --- p.107 / Appendix 5. Regression Results for Housing Attributes from Literature --- p.113 / Bibliography --- p.115

In the first essay, this thesis provides a new methodology for pricing the fixed income derivatives using the arbitrage-free Heath-Jarrow-Morton model (hereafter HJM model). While, most previous empirical implementations of HJM model like that by Amin and Morton (1994) are focused on one-factor model only, the essay attempts to extend the test to a two-factor model that could further capture the subtleties of the forward rate process. The two-factor Poisson-Gaussian version of HJM model derived by Das (1999) that incorporates a jump component as the second state variables is used to value the actively traded Eurodollar futures call option under the jump diffusion lattice. The one-factor and two-factor models are compared with five volatility functions to evaluate the degree of pricing improvement by the inclusion of one more state variable. / The essay also addresses the critical issues on the volatility structure of forward rates that affect the pricing performance of option under the HJM framework. Three new volatility specifications are constructed to estimate the traded options. The first volatility function is the humped & curvature adjusted model that allows for humped shape in volatility structure and better adjustment to the curvature of the term structure. The second is the humped & proportional model that exhibits humped volatility feature and is proportional to the forward rate. The third function is the linear exponential model that is extended from Vasicek's exponential model. They are compared with two other volatility structures developed by previous researchers on their pricing performances. The alternative models are examined from the perspectives of in-sample fit, out-of-sample pricing and hedging. / The second essay develops an approach for estimating the Value-at-Risk (hereafter VaR) with jumps using the Monte Carlo simulation method. It is by far the first paper to estimate VaR using the HJM model. The paper takes the framework of the Poisson Gaussian version of HJM model (hereafter, HJM jump-diffusion model) from Das (1999). The model is incorporated with a jump component to capture the kurtosis effect in the daily price changes. As a result, the HJM jump-diffusion model allows for the fat tailed and skewed distribution of return in most financial markets. The simulation process is expedited by using variance reduction method. The model is used for calculating the VaR of a portfolio consisting of the fixed income derivatives. The accuracy of the VaR estimates is examined statistically at the VaR at confidence level of both 95 and 99 percent. / This thesis is a collection of two essays that explore issues related to the pricing and the risk management of fixed income securities and derivatives in US markets. In the context of the pricing of derivatives, the arbitrage-free pricing approach is adopted. For the issue of risk management, the estimation of Value-at-Risk is presented. / by Ze-To Yau Man. / Source: Dissertation Abstracts International, Volume: 62-09, Section: A, page: 3138. / Supervisors: Jia He; Ying-foon Chow. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 145-151). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

This dissertation is an empirical study of demand and supply in differentiated products markets using supermarket scanner data on two particular product categories - canned tuna and hot-breakfast cereals. First, I study the impact of retailers' price promotions on consumer demand and retailer profits in the canned-tuna product category. Since canned tuna is storable, I examine whether consumers stock up during sales. The results suggest that only a limited amount of stockpiling exists in this product category. Since inventory is not very important, consumer demand is thus modeled by a static demand model with a random-coefficients-nested-logit specification, which is estimated by the Markov Chain Monte Carlo method. The unit-sales decomposition results show that on average 36% of the demand response to price promotions comes from brand-switching, so market expansion effects due to consumers switching from the outside good and to higher quantities usually dominate the brand-switching effect. Using the demand estimates, I compute optimal retail prices assuming that stores are local monopolists and choose prices to maximize static category-level profits. I find that regular prices at "high-low" stores are typically at or slightly below the optimal prices, but that regular prices at "every-day-low-price" stores are substantially below the optimal prices. These results suggest that retail price levels and price promotions are more likely related to local market conditions such as retail competition. In addition, I study the effects of store-brand (SB) entry on the demand elasticities of incumbent national brands (NB), consumers' substitution patterns for national and store brands, and the implications for consumer welfare in the hot-breakfast-cereals product category. A random-coefficients model of consumer demand is estimated by the generalized-method-of-moments approach. The empirical findings are: (1) After the entry of SB's, demand becomes more elastic for non-imitated NB's, and either more elastic or shows no change for imitated NB's; (2) in general, substitution patterns for NB's and SB's are asymmetric, i.e., when the prices of their favorite products increase, most NB buyers tend to substitute to other NB products, but SB buyers will substitute to the corresponding imitated NB's; (3) the increase in consumer surplus due to SB entry is trivial for an individual consumer, but the aggregate benefit could be quite substantial.

This thesis explores continuous-time reinforcement learning (RL) for stochastic control with two intimately related problems: mean-variance (MV) portfolio selection and linear-quadratic (LQ) control. For the former, we investigate markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes yet the coefficients of these processes are unknown. Based on the recently developed RL theory for diffusion processes, we present data-driven algorithms that learns the pre-committed investment strategies directly without attempting to learn or estimate the market coefficients. For multi-stock Black–Scholes markets without factors, we develop a baseline algorithm and prove its performance guarantee by deriving a sublinear regret bound in terms of the Sharpe ratio. To optimize performance and facilitate real-world application, we further adapt the baseline algorithm into four variants. These enhancements incorporate techniques such as real-time online learning, offline pre-training, and mechanisms for managing leverage constraints and trading frequency. Following this, we perform a comprehensive empirical study to compare our RL algorithms against fifteen established portfolio allocation strategies based on S&P 500 constituents. The study employs multiple performance metrics, including annualized returns, variations of the Sharpe ratio, maximum drawdown, and recovery time. The results demonstrate that our continuous-time RL strategies are consistently among the best especially in a volatile bear market, and decisively outperform the model-based continuous-time counterparts by significant margins. We next study RL for a class of continuous-time LQ control problems for diffusions, where states are scalar-valued and running control rewards are absent but volatilities of the state processes depend on both state and control variables. We apply a model-free approach that relies neither on knowledge of model parameters nor on their estimations, and devise an actor--critic algorithm to learn the optimal policy parameter directly. Our main contributions include the introduction of an exploration schedule and a regret analysis of the proposed algorithm. We provide the convergence rate of the policy parameter to the optimal one, and prove that the algorithm achieves a regret bound of 𝑂(𝑁³/⁴) up to a logarithmic factor, where N is the number of learning episodes. We conduct a simulation study to validate the theoretical results and demonstrate the effectiveness and reliability of the proposed algorithm. We also perform numerical comparisons between our method and those of the recent model-based stochastic LQ RL studies adapted to the state- and control-dependent volatility setting, demonstrating a better performance of the former in terms of regret bounds. Along a different direction, we present a policy gradient-based actor–critic algorithm featuring adaptive exploration in both actor and critic. To wit, both the variance of the stochastic policy (actor) and the temperature parameter (critic) are decreasing in time according to certain schedules. In particular, endogenizing the temperature parameter reduces the need for manual tuning. Despite this added flexibility, the algorithm maintains the same sublinear regret bound of 𝑂(𝑁³/⁴) as achieved in the deterministic schedule. In the numerical experiments, we evaluate the convergence rate and regret bound of the proposed algorithm, with results aligning closely with our theoretical findings.

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy