Master of Science / Department of Agricultural Economics / Ted C. Schroeder / Risk management decision makers face significant price risk when purchasing or selling wholesale beef. Previous research has identified cross-hedging wholesale beef in Live Cattle futures as a plausible means of reducing this risk. Changes in the way beef is marketed have led to poor performance of cross-hedging programs. Unlike earlier research, more recent studies have shown that Live Cattle futures are a poor venue for effective cross-hedging. This study replicates previous research to evaluate the current state of traditional cross-hedging performance. Focus then shifts to improving cross-hedging methods. Hedge ratios derived from a traditional cross-hedging methodology exhibit a great deal of sensitivity to season, estimation technique, and quality grade. Basis risk is abundant for this type of cross-hedging. To reduce the basis risk inherent with cross-hedging wholesale beef, bundling is proposed. This involves combining two or more cuts together in a single unit to be cross-hedged. Firms merchandising meat from a whole carcass would be able to provide a valuable risk management service if the basis risk faced when hedging a bundled product is less than the basis risk faced when cross-hedging the corresponding products independently. This research found that bundling has neither a positive or negative effect on basis risk. Therefore bundling is a plausible practice, but will not offer reduced basis risk to decision makers.

Submitted by Odilon Jose de Oliveira Neto (professorodilon@yahoo.com.br) on 2013-09-27T20:34:42Z No. of bitstreams: 1 TESE_ODILON.pdf: 885119 bytes, checksum: 460d85982ff9b027e21ee9ef445337e1 (MD5) / Approved for entry into archive by Vera Lúcia Mourão (vera.mourao@fgv.br) on 2013-09-27T20:50:10Z (GMT) No. of bitstreams: 1 TESE_ODILON.pdf: 885119 bytes, checksum: 460d85982ff9b027e21ee9ef445337e1 (MD5) / Made available in DSpace on 2013-09-27T21:19:03Z (GMT). No. of bitstreams: 1 TESE_ODILON.pdf: 885119 bytes, checksum: 460d85982ff9b027e21ee9ef445337e1 (MD5) Previous issue date: 2013-09-20 / Several attempts of negotiation of future contracts and price indexes of beef cattle in Argentina and in Uruguay were frustrated along the years. The derivatives issued failed in a short period of time due to lack of liquidity. That scenery and other particularities of the live cattle spot market turned the administration of risk of prices into a problem for the economical agents of the meat chain. In this context, the following question emerged: the cross hedging with future contracts of Brazilian live cattle in the Brazilian Securities, Commodities and Futures Exchange (BM&FBovespa) is effective for the administration of risk of prices of beef steers in the Argentinian and Uruguayan spot market? In an effort to answer this question, it was proposed to verify if it is possible to mitigate the risk of the price volatility of the spot market of Argentinian and Uruguayan beef steers through of cross hedging in the futures market for Brazilian live cattle in the BM&FBovespa. For this, it was used static and dynamic models to estimate of the optimal cross hedge ratio and effectiveness of risk mitigation. The results of the hypothesis test of risk mitigating allow to assure that there are strong empirical evidences of effectiveness of the futures market of Brazilian live cattle in protection against the prices risk of the spot market of Argentinian and Uruguayan steers. Complementarily, it was analyzed the hypothesis of the futures market efficiency. The results present empirical evidence of a stochastic relationship common in long-term between spot and futures prices, and efficiency in predicting short-term price, which suggest that the future contracts of Brazilian live cattle in the BM&FBovespa allow adequate hedge of price for the Argentinian and Uruguayan steers in spot market. / Na Argentina e no Uruguai, diversas tentativas de negociação de contratos futuros e de índice de preços de carne bovina foram frustradas ao longo dos anos, tendo os derivativos lançados fracassado, em um curto espaço de tempo, por falta de liquidez. Esse cenário, somado a outras particularidades do mercado físico da carne bovina, torna o gerenciamento de risco de preços um problema para os agentes econômicos que atuam nessa cadeia produtiva. Nesse contexto, emergiu a seguinte questão: a proteção cruzada com contratos futuros de boi gordo brasileiro da Bolsa de Valores, Mercadorias e Futuros de São Paulo (BM&FBovespa) é efetiva para a administração do risco de preços dos novilhos de corte no mercado a vista argentino e uruguaio? Com a finalidade de responder a essa questão, propôs-se a verificar se é possível mitigar o risco da volatilidade de preços no mercado a vista dos novilhos de corte argentinos e uruguaios por meio do cross hedging no mercado futuro do boi gordo brasileiro na BM&FBovespa. Para tanto, foram utilizados modelos estáticos e dinâmicos de estimação da razão de cross hedge ótima e efetividade em mitigação do risco. Os resultados do teste de hipóteses de mitigação do risco permitiram assegurar que são fortes as evidências de efetividade do mercado futuro do boi gordo brasileiro na proteção contra o risco de preços do mercado a vista dos novilhos argentinos e uruguaios. Complementarmente, verificou-se a hipótese de eficiência do mercado futuro. Os resultados apresentaram evidências de um relacionamento estocástico comum no longo prazo entre os preços a vista e futuros, e de eficiência na predição dos preços no curto prazo, o que sugere que os contratos futuros de boi gordo brasileiro da BM&FBovespa permitem uma trava adequada de cotação-preço para os novilhos argentinos e uruguaios no mercado a vista.

Im ersten Teil der Arbeit analysieren wir BSDEs mit Generatoren, die monoton in y, convex in z, gemeinsam unterhalbstetig und von unten durch eine affine Funktion der Kontrollvariable beschränkt sind. Das erste Hauptresultat ist der Nachweis der Existenz und Eindeutigkeit einer minimalen Superlösung. Wir zeigen, dass für die minimale Superlösung wichtige Eigenschaften, wie zum Beispiel die Flusseigenschaft und die Projektivität gelten. Es stellt sich heraus, dass das Funktional welches die Endbedingung auf das Infimum über alle Wertprozesse zur Zeit null abbildet nicht nur den gleichen Definitionsbereich wie der Erwartungswert hat, sondern auch einige seiner wichtigsten Eigenschaften, wie monotone Konvergenz und Fatou''s Lemma teilt. Das führt im Weiteren zur Unterhalbstetigkeit und zu dualen Darstellungen dieses Funktionals. Schlussendlich zeigen wir eine Lösung des Nutzenmaximierungsproblems für die Exponentialnutzenfunktion. Im zweiten Teil der Arbeit untersuchen wir die quadratische Absicherung von finanziellen Risikopositionen unter Basisrisiko. Zuerst zeigen wir wie optimal abgesichert wird, wenn die Differenz der Logarithmen von Absicherungsinstrument und Risiko asymptotisch stationär ist. Für lineare Risikopositionen leiten wir explizite Formeln für den Absicherungsfehler her und zeigen, dass für nichtlineare Positionen eine schnelle Simulation möglich ist. Zweitens untersuchen wir ein Modell in dem die Korrelation zwischen Absicherungsinstrument und Basiswert stochastisch ist. Wir nehmen an, dass die Korrelation ein Prozess ist, der sich gemäß einer stochastischen Differentialgleichung mit Werten zwischen -1 und 1 entwickelt. Wir leiten eine Integrabilitätsbedingung bezüglich des Korrelationsprozesses her, die uns erlaubt die optimale quadratische Absicherung durch eine einfache Formel zu beschreiben. Weiterhin zeigen wir, dass unsere Bedingungen von einer großen Klasse von Korrelationsdynamiken erfüllt werden. / In the first part of the thesis we analyze BSDEs with generators that are monotone in y, convex in z, jointly lower semicontinuous, and bounded below by an affine function of the control variable. The first central result establishes existence and uniqueness of a minimal supersolution. We show that our setting allows to derive important properties of the minimal supersolution such as the flow property and the projectivity. We find that the functional which maps the terminal condition to the infimum over all value processes evaluated at time zero is not only defined on the same domain as the original expectation operator, but also shares some of its main properties such as monotone convergence and Fatou''s Lemma. Moreover, this leads to lower semincontinuity and dual representations of the functional. Finally, we demonstrate a solution of the problem of maximizing expected exponential utility. In the second part of the thesis we investigate quadratic hedging of contingent claims with basis risk. We first show how to optimally cross-hedge risk when the logspread between the hedging instrument and the risk is asymptotically stationary. For linear risk positions we derive explicit formulas for the hedge error, while for non-linear positions swift simulation analysis is possible. Secondly, we study a model where the correlation between the hedging instrument and the underlying of the contingent claim is random itself. We assume that the correlation is a process which evolves according to a stochastic differential equation with values between the boundaries -1 and 1. We derive an integrability condition on the correlation process that allows to describe the quadratic hedge by means of a simple hedging formula. Furthermore we show that our conditions are fulfilled by a large class of correlation dynamics.

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: We consider the utility portfolio optimization problem of an investor whose activities are influenced by an exogenous financial risk (like bad weather or energy shortage) in an incomplete financial market. We work with a fairly general non-Markovian model, allowing stochastic correlations between the underlying assets. This important problem in finance and insurance is tackled by means of backward stochastic differential equations (BSDEs), which have been shown to be powerful tools in stochastic control. To lay stress on the importance and the omnipresence of BSDEs in stochastic control, we present three methods to transform the control problem into a BSDEs. Namely, the martingale optimality principle introduced by Davis, the martingale representation and a method based on Itô-Ventzell’s formula. These approaches enable us to work with portfolio constraints described by closed, not necessarily convex sets and to get around the classical duality theory of convex analysis. The solution of the optimization problem can then be simply read from the solution of the BSDE. An interesting feature of each of the different approaches is that the generator of the BSDE characterizing the control problem has a quadratic growth and depends on the form of the set of constraints. We review some recent advances on the theory of quadratic BSDEs and its applications. There is no general existence result for multidimensional quadratic BSDEs. In the one-dimensional case, existence and uniqueness strongly depend on the form of the terminal condition. Other topics of investigation are measure solutions of BSDEs, notably measure solutions of BSDE with jumps and numerical approximations. We extend the equivalence result of Ankirchner et al. (2009) between existence of classical solutions and existence of measure solutions to the case of BSDEs driven by a Poisson process with a bounded terminal condition. We obtain a numerical scheme to approximate measure solutions. In fact, the existing self-contained construction of measure solutions gives rise to a numerical scheme for some classes of Lipschitz BSDEs. Two numerical schemes for quadratic BSDEs introduced in Imkeller et al. (2010) and based, respectively, on the Cole-Hopf transformation and the truncation procedure are implemented and the results are compared. Keywords: BSDE, quadratic growth, measure solutions, martingale theory, numerical scheme, indifference pricing and hedging, non-tradable underlying, defaultable claim, utility maximization. / AFRIKAANSE OPSOMMING: Ons beskou die nuts portefeulje optimalisering probleem van ’n belegger wat se aktiwiteite beïnvloed word deur ’n eksterne finansiele risiko (soos onweer of ’n energie tekort) in ’n onvolledige finansiële mark. Ons werk met ’n redelik algemene nie-Markoviaanse model, wat stogastiese korrelasies tussen die onderliggende bates toelaat. Hierdie belangrike probleem in finansies en versekering is aangepak deur middel van terugwaartse stogastiese differensiaalvergelykings (TSDEs), wat blyk om ’n onderskeidende metode in stogastiese beheer te wees. Om klem te lê op die belangrikheid en alomteenwoordigheid van TSDEs in stogastiese beheer, bespreek ons drie metodes om die beheer probleem te transformeer na ’n TSDE. Naamlik, die martingale optimaliteits beginsel van Davis, die martingale voorstelling en ’n metode wat gebaseer is op ’n formule van Itô-Ventzell. Hierdie benaderings stel ons in staat om te werk met portefeulje beperkinge wat beskryf word deur geslote, nie noodwendig konvekse versamelings, en die klassieke dualiteit teorie van konvekse analise te oorkom. Die oplossing van die optimaliserings probleem kan dan bloot afgelees word van die oplossing van die TSDE. ’n Interessante kenmerk van elkeen van die verskillende benaderings is dat die voortbringer van die TSDE wat die beheer probleem beshryf, kwadratiese groei en afhanglik is van die vorm van die versameling beperkings. Ons herlei ’n paar onlangse vooruitgange in die teorie van kwadratiese TSDEs en gepaartgaande toepassings. Daar is geen algemene bestaanstelling vir multidimensionele kwadratiese TSDEs nie. In die een-dimensionele geval is bestaan ââen uniekheid sterk afhanklik van die vorm van die terminale voorwaardes. Ander ondersoek onderwerpe is maatoplossings van TSDEs, veral maatoplossings van TSDEs met spronge en numeriese benaderings. Ons brei uit op die ekwivalensie resultate van Ankirchner et al. (2009) tussen die bestaan van klassieke oplossings en die bestaan van maatoplossings vir die geval van TSDEs wat gedryf word deur ’n Poisson proses met begrensde terminale voorwaardes. Ons verkry ’n numeriese skema om oplossings te benader. Trouens, die bestaande self-vervatte konstruksie van maatoplossings gee aanleiding tot ’n numeriese skema vir sekere klasse van Lipschitz TSDEs. Twee numeriese skemas vir kwadratiese TSDEs, bekendgestel in Imkeller et al. (2010), en gebaseer is, onderskeidelik, op die Cole-Hopf transformasie en die afknot proses is geïmplementeer en die resultate word vergelyk.

Submitted by Alexander Buck (alexanderwolfram.buck@student.unisg.ch) on 2017-12-13T18:40:57Z No. of bitstreams: 1 Alexander Buck_Masters Thesis.pdf: 814162 bytes, checksum: 581ec59995af7545d603be8b2da6e30e (MD5) / Rejected by Josineide da Silva Santos Locatelli (josineide.locatelli@fgv.br), reason: Dear Alexander, There are some corrections to do in your thesis, please, see below: Page 2: in Knowledge Field, put your advisor field: Economia E Finanças Internacionais; Page 4: in Knowledge Field, put your advisor field: Economia E Finanças Internacionais; ACKNOWLEDGMENT, Abstract, Resumo and Contents must be in capital letters and in the middle of the page. After corrections, please, post again. on 2017-12-14T11:20:17Z (GMT) / Submitted by Alexander Buck (alexanderwolfram.buck@student.unisg.ch) on 2017-12-14T11:42:06Z No. of bitstreams: 1 Alexander Buck_Masters Thesis.pdf: 814627 bytes, checksum: 3f642bd3522c9184319e19ef0fc4d2b4 (MD5) / Approved for entry into archive by Josineide da Silva Santos Locatelli (josineide.locatelli@fgv.br) on 2017-12-14T12:22:33Z (GMT) No. of bitstreams: 1 Alexander Buck_Masters Thesis.pdf: 814627 bytes, checksum: 3f642bd3522c9184319e19ef0fc4d2b4 (MD5) / Made available in DSpace on 2017-12-14T12:31:14Z (GMT). No. of bitstreams: 1 Alexander Buck_Masters Thesis.pdf: 814627 bytes, checksum: 3f642bd3522c9184319e19ef0fc4d2b4 (MD5) Previous issue date: 2017-11-23 / Financial derivatives are broadly used for hedging purposes by large financial and non-financial corporations in developed countries. Thereof, currency derivatives represent the biggest class. For some currencies, foreign exchange exposure, for example arising from exports or foreign investments, cannot be hedged due to illiquid or nonexistent derivative markets. However, a third currency with liquid derivative markets exists and can be used to cross-hedge the exposure. This thesis examines whether using options with multiple strikes can improve the hedging performance in such a case. Several stochastic models commonly applied in the literature to foreign exchange markets are used for the out-of-sample hedging portfolio construction and applied to currencies in the regions Latin America, Europe and East/Southeast Asia between 2012 and 2016. This paper delivers two main results: Firstly, it is shown that adding options is not beneficial mainly due to model and estimation errors which increase risk. Secondly, it is shown that if the US-Dollar exchange rate is not cross-hedgeable, the exchange rate with the third currency must be, unless the foreign currency is highly volatile. As a consequence, cross-hedging can be successfully applied to at least one of those exchange rates. However, it is optimal to use only forwards in that case. / Derivativos financeiros são amplamente utilizados com finalidade de hedge por grandes corporações financeiras e não-financeiras em países desenvolvidos. Nesse sentido, derivativos de câmbio representam a classe mais expressiva. Para algumas moedas, a exposição cambial resultante por exemplo de exportações ou investimentos externos não pode ser coberta devido à iliquidez ou inexistência de mercados de derivativos. No entanto, existe um terceiro câmbio de mercados de derivativos líquidos que pode ser utilizado para cobrir a exposição cambial com cross-hedge. A presente tese examina se o uso de opções com múltiplos preços de exercício pode melhorar o desempenho de hedge em tal caso. Vários modelos estocásticos comumente aplicados na literatura a mercados de câmbio são utilizados para a construção out-of-sample de um portfolio de hedging e aplicados a câmbios na América Latina, Europa e Leste/Sudeste asiático entre 2012 e 2016. Esse trabalho chega a dois resultados centrais. O primeiro demonstra que não é benéfico adicionar opções sobretudo em virtude de erros de modelo e estimativa que elevam riscos. O segundo demonstra que se a taxa de câmbio do dólar americano não permite cross-hedging, a taxa de câmbio do terceiro câmbio precisa permitir, a menos que a moeda estrangeira seja altamente volátil. Consequentemente, cross-hedging pode ser aplicado com sucesso a pelo menos uma destas taxas de câmbio. Entretanto, é aconselhável utilizar apenas forwards nesse caso.

在利率自由化的過程中，貨幣市場利率變化情形較以前劇烈，因此近年來 使得一些需要運用貨幣市場來融通短期資金的廠商與個人較以往面臨更大 的利率變動的風險。本文的主要目的在探討以芝加哥期貨交易所(CBOT)之 美國長期公債期貨合約、十年期公債期貨合約及五年期公債期貨合約及芝 加哥商品期貨交易所(CME) 的美國國庫券期貨、Eurodollar期貨之組合交 叉規避國內商業本票30天期、90天期、 180天期之次級市場的利率風險， 以了解利用國外利率期貨交叉規國內商業本票現貨利率風險的績效及不同 的避險期間與不同的避險比例對避險績效的影響。本研究之採樣期間 自1989年 1月至1992年10月底，並分為兩部份進行實證，一為整體樣本測 試避險模式、另一為樣本外交叉避險模式，且修正自身相關現象。 根據 實證結果，可以得到以下的結論與發現：1.在整體樣本測試交叉避模式之 自身相關迴歸分析中，當避險期間愈長時，則避險績效愈好。2.在樣本外 測試交叉避險模式--最適避險模式之價差迴歸分析與自身相關迴歸分析中 ，可以發現三種商業本票的交叉避險績效均以避險期間較短者擁有較好的 交叉避險績效。3.在樣本外測試交叉避險模式中，所有商業本票不論何種 避險期間，自然避險模式的交叉避險績效均比最適避險模式為差。4.在樣 本外測試交叉避 險模式--最適避險模式之價差迴歸分析與自身相關迴歸 分析中，可以發現所有商業本票，在單一期貨組合的交叉避險績效大致上 皆高於其他期貨組合的交叉避險績效，因此，在從事避險操作時，基於時 間及交易成本的考量，以單一期貨組合從事避險操作較為有利。