I study retail prices of sport goods for a particular multinational producer across European countries and in the USA to examine behaviour of the law of one price. Although average prices across all goods in the sample differ only slightly across most of the countries, I find significant price differences for individual goods for almost each country pair, including a group of the states that are generally considered as relatively integrated. The conducted analysis has not confirmed that these differences are caused primarily by various distribution costs. The computed relative prices across products vary significantly once compared internationally even within a group of similar goods of which distribution costs should be the same. The price variation, which prevails even when costs are excluded, points to the existence of strategic pricing and lagging arbitrage.

Hipóteses precisas são características naturais das teorias econômicas de determinação do valor ou preço de ativos financeiros. Nessas teorias, a precisão das hipóteses assume a forma do conceito de equilíbrio ou da não arbitragem. Esse último possui um papel fundamental nas teorias de finanças. Sob certas condições, o Teorema Fundamental do Apreçamento de Ativos estabelece um sistema único e coerente para valorização dos ativos em mercados não arbitrados, valendo-se para tal das formulações para processos de martingal. A análise da distribuição estatística desses ativos financeiros ajuda no entendimento de como os participantes se comportam nos mercados, gerando assim as condições para se arbitrar. Nesse sentido, a tese defendida é a de que o estudo da hipótese de não arbitragem possui contrapartida científica, tanto do lado teórico quanto do empírico. Utilizando-se do modelo estocástico Variância Gama para os preços dos ativos, o teste Bayesiano FBST é implementado com o intuito de se verificar a existência da arbitragem nos mercados, potencialmente expressa nos parâmetros destas densidades. Especificamente, a distribuição do Índice Bovespa é investigada, com os parâmetros risco-neutros sendo estimados baseandose nas opções negociadas no Segmento de Ações e no Segmento de Derivativos da BM&FBovespa. Os resultados aparentam indicar diferenças estatísticas significantes em alguns períodos de tempo. Até que ponto esta evidência é a expressão de uma arbitragem perene nesses mercados ainda é uma questão em aberto. / Precise hypotheses are natural characteristics of the economic theories for determining the value or prices of financial assets. Within these theories the precision is expressed in terms of equilibrium and non-arbitrage hypotheses. The former concept plays an essential role in the theories of finance. Under certain conditions, the Fundamental Theorem of Asset Pricing establishes a coherent and unique asset pricing framework in non-arbitraged markets, grounded on martingales processes. Accordingly, the analysis of the statistical distributions of financial assets can assist in understanding how participants behave in the markets, and may or may not engender conditions to arbitrage. On this regard, the dissertation proposes that the study of non-arbitrage hypothesis has a scientific counterparty, theoretically and empirically. Using a variance gamma stochastic model for prices, the Bayesian test FBST is conducted to verify the presence of arbitrage potentially incorporated on these densities parameters. Specifically, the Bovespa Index distribution is investigated, with risk neutral parameters estimated based on options traded in the Equities Segment and the Derivatives Segment at the BM&FBovespa Exchange. Results seem to indicate significant statistical differences at some periods of time. To what extent this evidence is actually the expression of a perennial arbitrage between the markets still is an open question.

Xiong, Liying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leave 34). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Hong Kong Horse Racing Market and Models in Horse Racing --- p.3 / Chapter 2.1 --- Hong Kong Horse Racing Market --- p.4 / Chapter 2.2 --- Models in Horse Racing --- p.5 / Chapter 3 --- Probit Regression Model Incorporating with Public Estimates --- p.9 / Chapter 3.1 --- Estimation under No Particular Conditions --- p.10 / Chapter 3.2 --- Estimators under Particular Condition --- p.15 / Chapter 4 --- Prediction and Testing --- p.23 / Chapter 4.1 --- Prediction of Win Probability --- p.24 / Chapter 5 --- Conclusion --- p.32 / Bibliography --- p.34

I investigate a simple merger arbitrage strategy with a focus on middle-market companies. I estimate [-1, 1] buy-and-hold abnormal returns (BHARs) and long-run BHARs of prospective middle-market acquirers after they announce an acquisition and test whether [-1, 1] BHARs are predictive of subsequent long-run holding period returns (HPRs) and long-run BHARs. The [-1, 1] BHARs are calculated for 57 acquiring companies, and then separated into two equal-weight portfolios: one of positive [-1, 1] BHARs (referred to as the long portfolio) and one of negative [-1, 1] BHARs (referred to as the short portfolio). I then calculate the HPR and long-run BHARs over the following time horizons: [2, 22], [2, 43], [2, 64], [2, 127], and [2, 253]. I perform a Student’s t-test comparing the means of the HPRs of the two portfolios and find that the long and short [2, 22] and [2, 64] HPRs have statistically different mean returns. Similarly, I perform a Student’s t-test comparing the means of the BHARs of the two portfolios and find that the difference in the means are not statistically significant. I also regress the different long-run BHARs on [-1, 1] BHARs, adjusted [-1, 1] BHARs, and normalized [-1, 1] BHARs. Adjusted [-1, 1] BHARs are adjusted for the effects of known predictive factors found in prior literature such as the type of payment. For example, if the type of payment is cash, 2.40 percentage points of the [-1, 1] BHAR is attributed to the cash payment. Normalized [-1, 1] BHARs divide each [-1, 1] BHAR by each security return’s standard deviation over the following trading days: [-22, -2]. I find [-1, 1] BHARs and adjusted [-1, 1] BHARs of middle-market lack statistically significant effects on long-run BHARs over the [2, 22], [2, 43], [2, 127], and [2, 253] horizons. [-1, 1] BHARs and adjusted [-1, 1] BHARs of middle-market firms have statistically significant effects on [2, 64] BHARs. Therefore, a possible merger arbitrage strategy may exist for predicting BHARs for the [2, 64] horizon. The strategy consists of an investor going long on all acquirers that have a positive [-1, 1] BHAR and short on all acquirers that have a negative [-1, 1] BHAR over the following trading days: [2, 64]. After the [-1, 1] BHARs are normalized, however, the normalized [-1, 1] BHARs are no longer statistically significant when predicting any long-run BHAR. On the whole, I find the Efficient Market Hypothesis – which states that the market efficiently prices the information released into the market after an acquisition announcement – is correct, at least with respect to the information contained in [-1, 1] BHARs.

The Black-Scholes model is one of the most important concepts in modern financial theory. It was developed in 1973 by Fisher Black, Robert Merton and Myron Scholes and is still widely used today, and regarded as one of the best ways of determining fair prices of options. In the classical Black-Scholes model for the market, it consists of an essentially riskless bond and a single risky asset. So far there is a number of straightforward extensions of the Black-Scholes analysis. Here we consider more complex products where each component in a portfolio entails several variables with constraints. This leads to elegant models based on multivariable stochastic integration, and describing several securities simultaneously. We derive a general asymptotic solution in a short time interval using the heat kernel expansion on a Riemannian metric. We then use our formula to predict the better price of options on multiple underlying assets. Especially, we apply our method to the case known as the one of two-color rainbow ptions, outperformance option, i.e., the special case of the model with two underlying assets. This asymptotic solution is important, as it explains hidden effects in a class of financial models.

Cette thèse porte sur les méthodes numériques pour les équations aux dérivées partielles (EDP) non-linéaires dégénérées, ainsi que pour des problèmes de contrôle d'EDP non-linéaires résultants d'un nouveau problème de transport optimal. Toutes ces questions sont motivées par des applications en mathématiques financières. La thèse est divisée en quatre parties. Dans une première partie, nous nous intéressons à la condition nécessaire et suffisante de la monotonie du $\theta$-schéma de différences finies pour l'équation de diffusion en dimension un. Nous donnons la formule explicite dans le cas de l'équation de la chaleur, qui est plus faible que la condition classique de Courant-Friedrichs-Lewy (CFL). Dans une seconde partie, nous considérons une EDP parabolique non-linéaire dégénérée et proposons un schéma de type ''splitting'' pour la résoudre. Ce schéma réunit un schéma probabiliste et un schéma semi-lagrangien. Au final, il peut être considéré comme un schéma Monte-Carlo. Nous donnons un résultat de convergence et également un taux de convergence du schéma. Dans une troisième partie, nous étudions un problème de transport optimal, où la masse est transportée par un processus d'état type ''drift-diffusion'' controllé. Le coût associé est dépendant des trajectoires de processus d'état, de son drift et de son coefficient de diffusion. Le problème de transport consiste à minimiser le coût parmi toutes les dynamiques vérifiant les contraintes initiales et terminales sur les distributions marginales. Nous prouvons une formule de dualité pour ce problème de transport, étendant ainsi la dualité de Kantorovich à notre contexte. La formulation duale maximise une fonction valeur sur l'espace des fonctions continues bornées, et la fonction valeur correspondante à chaque fonction continue bornée est la solution d'un problème de contrôle stochastique optimal. Dans le cas markovien, nous prouvons un principe de programmation dynamique pour ces problèmes de contrôle optimal, proposons un algorithme de gradient projeté pour la résolution numérique du problème dual, et en démontrons la convergence. Enfin dans une quatrième partie, nous continuons à développer l'approche duale pour le problème de transport optimal avec une application à la recherche de bornes de prix sans arbitrage des options sur variance étant donnés les prix des options européennes. Après une première approximation analytique, nous proposons un algorithme de gradient projeté pour approcher la borne et la stratégie statique correspondante en options vanilles.

This work mainly studies modeling and existence issues for martingale models of option markets with one stock and a collection of European call options for one fixed maturity and infinetely many strikes. In particular, we study Dupire's and Schweizer-Wissel's models, especially the latter one. These two types of models have two completely different pricing approachs, one of which is martingale approach (in Dupire's model), and other one is a market approach (in Schweizer-Wissel's model). After arguing that Dupire's model suffers from the several lacks comparing to Schweizer-Wissel's model, we extend the latter one to get the variations for the case of options on interest rate indexes and futures options. Our models are based on the newly introduced definitions of local implied volatilities and a price level proposed by Schweizer and Wissel. We get explicit expressions of option prices as functions of the local implied volatilities and the price levels in our variations of models. Afterwards, the absence of the dynamic arbitrage in the market for such models can be described in terms of the drift restrictions on the models' coefficients. Finally we demonstrate the application of such models by a simple example of an investment portfolio to show how Schweizer-Wissel's model works generally.

Purpose: The purpose of this study is to increase the understanding of how a bank’s features and internal factors have affected its choice of method in calculating the capital requirement. Theoretical and Empirical Method: The research strategy of this study has been of a qualitative nature with a deductive approach. The choice of method was depth interviews with respondents from a targeted sample of Swedish banks. These respondents were chosen based on the knowledge they possess as key employees in the capital requirement process and their involvement in choosing their banks’ method for calculating the capital requirement. The interviews were semi-structured, with open questions that allowed a dialogue with the respondents in which they could express their opinions and knowledge regarding the factors affecting their banks’ choice of method. Theoretical Approach: The study is based on the new institutional economics theory of how institutions affect organizational behavior. It’s also based on earlier research within the regulation Basel II by, among others, Hakenes and Schabel (2011), Rime (2005) and Wahlström (2009). Conclusions: The results of this study show that banks have identified different factors that affect their choice of calculation method for the capital requirement. The choice the banks are facing is to keep the standardized method, develop an advanced internal based method, create partnerships with other banks or focus on alternative clientele portfolios. The two factors that were considered to be have the greatest significant for the choice of calculation method were resources associated with the implementation of the IRB approach models and how the banks’ clientele portfolio was designed. How these were distributed and to what extent they influenced the choice was highly individual for the chosen banks. / Syfte: Syftet med den här studien är att öka förståelsen om hur en banks förutsättningar och interna faktorer har påverkat dess val av beräkningsmetod för kapitalkravet. Teoretisk och empirisk metod: Forskningsstrategin för studien har varit av den kvalitativa typen med en deduktiv ansats. Valet av metod var djupintervjuer med respondenter från ett målinriktat urval av svenska banker. Respondenterna valdes utifrån de kunskaper som de besitter genom sin position på respektive bank, där deras deltagande i metodvalsprocessen påverkade valet av beräkningsmetod. Intervjuerna var av typen semistrukturerade, med öppna intervjufrågor för att få till en dialog med respondenterna och ta del av deras åsikter och kunskaper gällande de olika faktorerna till metodvalet. Teoretisk referensram: Studien utgick från den nyinstitutionella teorin, om hur institutioner påverkar organisationers beteenden. Den har baserats på tidigare forskning inom regelverket Basel II av bland annat Hakenes och Schnabel (2011), Rime (2005) samt Wahlström (2009). Slutsats: Resultatet av denna studie visar på att bankerna har identifierat olika faktorer som påverkar valet av beräkningsmetod för kapitalkravet. Valet som bankerna står inför är att behålla Schablonmetoden, utveckla en IRK-metod, skapa samarbeten med andra banker eller fokusera på alternativa klientelportföljer. De två faktorer som ansågs ha störst signifikans för valet av beräkningsmetod var resurserna som förknippades med implementeringen av modellerna i IRKmetoden och hur bankens klientelportfölj var utformad. Hur dessa var fördelade och i vilken grad de påverkade valet var högst individuellt för de utvalda bankerna.

In this thesis, we analyze premium relationship of American depositary receipts (ADR) and their underlying shares. Several researchers have previously identified the main variables influencing the construction of ADR premium of cross-listed companies. The aim of this study is to investigate to what extent the main variables affect differently the construction of ADR premium in crisis period. For the purpose of the study, two periods are defined. The period from June 2006 to October 2007 represents the non-crisis period whereas the period from October 2007 to March 2009 represents the crisis period. Our cross-listing sample consists of companies that have level II and level III ADR listed on the NYSE and the NASDAQ over the two periods. The tested variables influencing the premium are the liquidity, the currency exchange rate, the home and US market and the volatility. The liquidity is measured according to two ratios, the Amihud ratio and the turnover ratio. The currency exchange rate is the current exchange rate denominated in US dollar. The home markets are the reference indexes of the home country to which the underlying share of the ADR belong. The S&P 500 Index is used as a proxy for the US market. Finally, the US market volatility is analyzed with the CBOE VIX volatility Index. Multiple and simple OLS regressions are used to analyze the impacts of variables on ADR premium. The T-statistic is chosen to test the explanatory power of variables. The regressions are divided in three main parts. The first one is dedicated to the liquidity variables, then the second one to the home and US market, currency exchange rate and CBOE VIX volatility Index. Finally the last part keeps only the variables with the stronger explanatory power in order to define two equations of the factor influencing mostly the premium. We have found that crisis strongly modifies the relationship between ADR premium and the main variables. In crisis period, the regressions show that liquidity becomes a factor with a greater explanatory power of ADR premium. However the other main variables experience the opposite effect with a much lower T-test in times of crisis. It seems that the currency exchange rate, the home and US market as well as the volatility lose their explanatory power in times of crisis to the benefit of liquidity variables.

Contexte Le but de notre étude est d'expliquer les rendements des produits dérivés du baril de pétrole, de l'huile de chauffage, du gasoil, du café et du cacao en appliquant le modèle d'évaluation par arbitrage (MEA). Pour cela, nous avons constitué deux échantillons dont le premier commence en 1983 pour ce qui est de l'industrie pétrolière, et en 1966 pour les produits dérivés tropicaux. Le terme de la période d'étude est 2006. Les données ont une périodicité trimestrielle. Les variables que nous avons utilisés sont toutes liées à l'économie des États-Unis. Méthodologie et résultats La méthode du maximum de vraisemblance nous a permis de déterminer le pouvoir explicatif et les coefficients de sensibilité des différents modèles. Ainsi, nous avons constaté que le portefeuille du marché représenté ici par l'indice NYSE (New York Stock Exchange) n'est pas suffisant pour expliquer à lui seul les variations des rendements des actifs financiers. Les tests de student sur les primes de risque associées aux facteurs nous ont permis de constater que seul la prime de risque et le taux de croissance ne sont pas significatifs. Le test de maximum de vraisemblance appliqué a montré qu'il existe une relation linéaire entre les rendements expliqués et les facteurs. Conclusion Il ressort donc de notre étude que les sources de variations des produits dérivés sont multiples et de natures diverses. Constat qui rejoint l'idée fondamentale du MEA. Par ailleurs, l'utilisation de modèles macroéconomiques nous a permis de montrer que certaines « forces économiques » (l'inflation, le prix du pétrole, le portefeuille du marché, l'indice de production industrielle, la consommation per capita, les prix des commodités, la structure à terme) permettent de capter la volatilité des rendements étudiés. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Produits dérivés, Commodités, Matières premières, Volatilité, Rendements, Arbitrage.