Linkages between economic agents in form of financial assets might contribute to transmission of shocks between different parts of the economy. Aim of this thesis is to enrich the ongoing discussion about the spread of contagion through the economy. We provide an analysis of financial interlinkages in the Czech economy and using the contingent claims analysis (CCA) model we attempt to quantify risks in the system that that are implied by the existence of these linkages. We use different techniques within the framework of the model to obtain various indicators that can be used to assess stability of the system. Using simulations we find that size of losses due to riskiness of debt depends strongly on the origin of a shock and it is higher for shocks originating in the household sector than for shocks originating in the sector of the non-financial corporations. We also find that size of a decrease in capital of the banking sector needed to cause a distress in the system as relatively high and stable in time. JEL Classification E01, E44, G01, G12, G20 Keywords Balance sheet contagion, financial accounts, network models, contingent claims analysis, systemic risk Author's e-mail josef.brechler@gmail.com Supervisor's e-mail michal.hlavacek@cnb.cz

Neste trabalho, apresentamos um método de simulação Monte Carlo para o cálculo do hedging dinâmico de opções do tipo europeia em mercados multidimensionais do tipo Browniano e livres de arbitragem. Baseado em aproximações martingales de variação limitada para as decomposições de Galtchouk-Kunita-Watanabe, propomos uma metodologia factível e construtiva que nos permite calcular estratégias de hedging puras com respeito a qualquer opção quadrado integrável em mercados completos e incompletos. Uma vantagem da abordagem apresentada aqui é a flexibilidade de aplicação do método para os critérios quadráticos de minimização do risco local e de variância média de forma geral, sem a necessidade de se considerar hipóteses de suavidade para a função payoff. Em particular, a metodologia pode ser aplicada para calcular estratégias de hedging quadráticas multidimensionais para opções que dependem de toda a trajetória dos ativos subjacentes em modelos de volatilidade estocástica e com funções payoff descontínuas. Ilustramos nossa metodologia, fornecendo exemplos numéricos dos cálculos das estratégias de hedging para opções vanilla e opções exóticas que dependem de toda a trajetória dos ativos subjacentes escritas sobre modelos de volatilidade local e modelos de volatilidade estocástica. Ressaltamos que as simulações são baseadas em aproximações para os processos de preços descontados e, para estas aproximações, utilizamos o método numérico de Euler-Maruyama aplicado em uma discretização aleatória simples. Além disso, fornecemos alguns resultados teóricos acerca da convergência desta aproximação para modelos simples em que podemos considerar a condição de Lipschitz e para o modelo de volatilidade estocástica de Heston. / In this work, we present a Monte Carlo simulation method to compute de dynamic hedging of european-type contingent claims in a multidimensional Brownian-type and arbitrage-free market. Based on bounded variation martingale approximations for the Galtchouk-Kunita- Watanabe decomposition, we propose a feasible and constructive methodology which allows us to compute pure hedging strategies with respect to any square-integrable contingent claim in complete and incomplete markets. An advantage of our approach is the exibility of quadratic hedging in full generality without a priori smoothness assumptions on the payoff function. In particular, the methodology can be applied to compute multidimensional quadratic hedgingtype strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. We illustrate our methodology, providing some numerical examples of the hedging strategies to vanilla and exotic contingent claims written on local volatility and stochastic volatility models. The simulations are based in approximations to the discounted price processes and, for these approximations, we use an Euler-Maruyama-type method applied to a simple random discretization. We also provide some theoretical results about the convergence of this approximation in simple models where the Lipschitz condition is satisfied and the Heston\'s stochastic volatility model.

Since 1980, many convertible bonds have been issued by Swedish companies. Most of these issues have been aimed at the employees. The great number of these employee issues gave rise to a new tax law. This tax law made it necessary to obtain a value on a convertible bond certificate at issue. In the first part of the dissertation, the institutional setting for the issuing of convertible bonds in Sweden is discussed. The relevant tax laws and recommendations given by different organizations are described. Also other features related to the issues are described. Furthermore, an empirical study of convertible bonds issues to emplyees in listed companies is carried out. The main purpose of the study is to quantify the volume of convertible bond issues to employees which have defaulted. Issues with a nominal value of around 500 million Swedish Crowns have been involved in some form of default. In this study, several models are compared to investigate whether the choice of model for valuing convertible bonds is important. These models all fall within the framework of Contingent Claims Analysis. Contingent Claims Analysis is an option based technique for determining the value of a claim whose payoffs depend upon the development of one or several underlying variables. In the study, it is shown in great detail how to set up and use those models. It is shown that the choice of model is important for the value of a convertible bond in certain situations. Those situations are identified by an empirical study of Swedish convertible bonds and through sensitivity analysis. / <p>Diss. Stockholm : Handelshögskolan, 1993</p>

Neste trabalho, apresentamos um método de simulação Monte Carlo para o cálculo do hedging dinâmico de opções do tipo europeia em mercados multidimensionais do tipo Browniano e livres de arbitragem. Baseado em aproximações martingales de variação limitada para as decomposições de Galtchouk-Kunita-Watanabe, propomos uma metodologia factível e construtiva que nos permite calcular estratégias de hedging puras com respeito a qualquer opção quadrado integrável em mercados completos e incompletos. Uma vantagem da abordagem apresentada aqui é a flexibilidade de aplicação do método para os critérios quadráticos de minimização do risco local e de variância média de forma geral, sem a necessidade de se considerar hipóteses de suavidade para a função payoff. Em particular, a metodologia pode ser aplicada para calcular estratégias de hedging quadráticas multidimensionais para opções que dependem de toda a trajetória dos ativos subjacentes em modelos de volatilidade estocástica e com funções payoff descontínuas. Ilustramos nossa metodologia, fornecendo exemplos numéricos dos cálculos das estratégias de hedging para opções vanilla e opções exóticas que dependem de toda a trajetória dos ativos subjacentes escritas sobre modelos de volatilidade local e modelos de volatilidade estocástica. Ressaltamos que as simulações são baseadas em aproximações para os processos de preços descontados e, para estas aproximações, utilizamos o método numérico de Euler-Maruyama aplicado em uma discretização aleatória simples. Além disso, fornecemos alguns resultados teóricos acerca da convergência desta aproximação para modelos simples em que podemos considerar a condição de Lipschitz e para o modelo de volatilidade estocástica de Heston. / In this work, we present a Monte Carlo simulation method to compute de dynamic hedging of european-type contingent claims in a multidimensional Brownian-type and arbitrage-free market. Based on bounded variation martingale approximations for the Galtchouk-Kunita- Watanabe decomposition, we propose a feasible and constructive methodology which allows us to compute pure hedging strategies with respect to any square-integrable contingent claim in complete and incomplete markets. An advantage of our approach is the exibility of quadratic hedging in full generality without a priori smoothness assumptions on the payoff function. In particular, the methodology can be applied to compute multidimensional quadratic hedgingtype strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. We illustrate our methodology, providing some numerical examples of the hedging strategies to vanilla and exotic contingent claims written on local volatility and stochastic volatility models. The simulations are based in approximations to the discounted price processes and, for these approximations, we use an Euler-Maruyama-type method applied to a simple random discretization. We also provide some theoretical results about the convergence of this approximation in simple models where the Lipschitz condition is satisfied and the Heston\'s stochastic volatility model.

An in depth study of the pricing of Game contingent claims under a general diffusion market model, in which interest rate is non constant, is presented. With the idea of providing a few numerical examples of the valuation of such claims, we present a detailed description of a Bootstrapping procedure to obtain interest rate information from Swaps rates. We also present a Stripping procedure that can be used to obtain initial spot (caplet) volatility from Market quotes on Caps/FLoors. These methods are of general application and could be used in the calibration of diffusion models of interest rate. Then we show several examples of calibration of the Hull--White model of interest rates. Our calibration examples are later used in the numerical approximation of the value of a particular form of Game option.

Abstract Game contingent claims (GCCs), as introduced by Kifer (2000), are a generalization of American contingent claims where the writer has the opportunity to terminate the contract, and must then pay the intrinsic option value plus a penalty. In complete markets, GCCs are priced using no-arbitrage arguments as the value of a zero-sum stochastic game of the type described in Dynkin (1969). In incomplete markets, the neutral pricing approach of Kallsen and Kühn (2004) can be used. In Part I of this thesis, we introduce GCCs and their pricing, and also cover some basics of mathematical finance. In Part II, we present a new algorithm for valuing game contingent claims. This algorithm generalises the least-squares Monte-Carlo method for pricing American options of Longstaff and Schwartz (2001). Convergence proofs are obtained, and the algorithm is tested against certain GCCs. A more efficient algorithm is derived from the first one using the computational complexity analysis technique of Chen and Shen (2003). The algorithms were found to give good results with reasonable time requirements. Reference implementations of both algorithms are available for download from the author’s Github page https://github.com/del/ Game-option-valuation-library

Finding the optimal capital structure has been a relevant subject for many decades. Therehas for a long time been a discrepancy between observed leverage ratio and those proposedby theory, with many different theories suggested and developed throughout time. One ofthose theories is the Contingent Claims Analysis (CCA). Based initially on Black &amp; Scholes’option-pricing theory and formulas, and pioneered by Merton, the CCA-methodology hasthroughout the years been developed further and moved from pricing liabilities todetermining capital structures. The research and development on CCA-models have for thepast years mostly been on a theoretical level and less about its practical applicability. Thosefew applications that have been made were based on the U.S. market and companies.Ju and Ou-Yang developed one of the most recent CCA-methodologies in 2006,abbreviated as the JOY-model in this study. What distinguishes this model is its ability toshow the non-monotone relation of debt maturity and debt face amount through the morecomplex tradeoffs between tax benefits, bankruptcy costs and transactions cost. With a fewchanges made to it, and with almost all data from the Swedish market and companies, theJOY-model yields higher leverage ratios than what the 5 analyzed companies have today.The optimal leverage ratio, defined as debt value/firm value ranges from 10 – 40% and theoptimal debt maturity period is at 4 – 6 years. Out of all the model parameters, the long-runmean of the stochastic risk-free interest rate has the biggest impact on the final results. TheJOY-model and CCA in general are complex and resource intense models that need certainimprovements. Nonetheless, its overall potential is still promising.

我國過去以出口為導向的經貿政策，帶動了持續穩定的經濟成長並累積鉅額的外匯存底。近年來隨著經濟發展的日益蓬勃，國內的投資環境面臨了前所未有的衝擊；廠商為求企業之經營成長及競爭優勢，無不致力於降低生產成本，擴大市場規模，因此形成一股前往海外投資的熱潮。本文主要目的是利用「或有請求權法-購入選擇權(CallOption)」訂價理論分析國內出口廠商面對各項投資環境之不確定性因素衝擊時，如何決定「對外投資之最適時機」。因此，本文模型具有下列幾特點：（一）以個別廠商之觀點，探討對外投資之最適時機。（二）探討投資國及地主國生產成本相對變動時，對外投資最適時機之影響。（三）探討投資國及地主國外匯匯率變動時，對外投資最適時機之影響。（四）探討投資地主國享有對外優惠關稅待遇時，對本國廠商對外投資最適時機之影響。（五）探討廠商之研究發展成果與對外投資最適時機之影響。