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Η παρούσα μελέτη αναπτύσσει ένα διαρθρωτικό υπόδειγμα πολλαπλών περιόδων για την αποτίμηση του τραπεζικού χρέους μειωμένης εξασφάλισης (subdebt) υπό διαφορετικές ρυθμιστικές πολιτικές. Το υπόδειγμα παρέχει ένα πλήρες πλαίσιο ανάλυσης με το οποίο διάφοροι παράγοντες, όπως οι πιστωτικοί κίνδυνοι και οι κίνδυνοι επιτοκίου, τα χαρακτηριστικά της τράπεζας και οι ρυθμιστικές πολιτικές, επηρεάζουν τις τιμές των υποομολόγων. H εμπειρική έρευνα πραγματοποιείται στη Matlab χρησιμοποιώντας τις διακριτοποιημένες μορφές των δυναμικών των περιουσιακών στοιχείων, του επιτοκίου και των καταθέσεων της τράπεζας. Δημιουργούμε 50000 μονοπάτια όπου προεξοφλούμε την απόδοση του υποχρέους μέσω της μεθόδου Monte Carlo. Διαπιστώνεται ότι η εφαρμογή άμεσων διορθωτικών μέτρων (PCA) θα αυξήσει τις τιμές του υποομολόγου, ενώ η κεφαλαιακή ανοχή θα έχει τα αντίθετα αποτελέσματα. Τέλος Οι μεταβολές των τιμών του χρέους μειωμένης εξασφάλισης είναι πιο ευαίσθητες για βραχυπρόθεσμες ωριμάνσεις από ό,τι για μακροπρόθεσμες ως προς τις διαφορετικές κεφαλαιακές θέσεις της τράπεζας., This study develops a multi-period structural model to value bank subordinated debt (subdebt) under different regulatory policies. The model provides a complete framework for analyzing how various factors, such as credit and interest rate risks, bank characteristics and regulatory policies affect subdebt prices. The empirical research was performed in Matlab using the discretized forms of the bank's assets, interest rate and bank’s deposits. We generate 50000 paths where we discount the payoff of subdebt through the Monte Carlo method. It turns out that the implementation of prompt corrective action (PCA) will raise subdebt prices, while capital forbearance will have the opposite effects. Finally the changes of Subordinated debt prices are more sensitive for short-term maturities than for long-term maturities to different bank capital positions.

A questão de quanto um investidor está disposto a pagar por um terreno parte do estudo de viabilidade econômico-financeira de um possível empreendimento imobiliário naquele local, que é, tradicionalmente, analisado pelos métodos de valor presente líquido (VPL) e taxa interna de retorno (TIR). No entanto, nesses métodos de análise, não se fornece ao investidor a noção exata da volatilidade do seu retorno quanto a possíveis mudanças de planos por parte do incorporador e mudanças no mercado, que podem ocorrer entre a compra do terreno e a venda das unidades imobiliárias prontas. Com este trabalho, propôs-se olhar para o investimento no desenvolvimento de um empreendimento imobiliário, levando-se em consideração o prêmio da opção de se desenvolver um projeto de incorporação em um terreno após sua aquisição. O objetivo foi mostrar que ao considerar, na análise de viabilidade financeira, a volatilidade da probabilidade de venda das unidades imobiliárias, o retorno do investidor não é o mesmo que o previsto em uma análise de viabilidade padrão de mercado e que existe um valor de investimento para determinada faixa de risco que o investidor esteja disposto a assumir ao financiar o projeto. Calculou-se, portanto, o valor do prêmio da opção de realizar um empreendimento imobiliário a partir da variação da probabilidade de venda dos imóveis lançados em um caso real de incorporação. Os resultados são muito significantes para a tomada de decisão do investidor. A modelagem mostra que existia um prêmio de opção de quase duas vezes o valor que foi pago pelo terreno do empreendimento, no cenário econômico em questão, no entanto, revela que o investimento que prometia taxa de retorno de 31% a.a. de acordo com a análise de viabilidade do incorporador, pagaria somente 19% a.a. A dissertação propõe uma maior qualidade de informação ao investidor fornecendo os limites inferior e superior desta taxa de retorno esperada, para um intervalo de confiança de 95% e, também, demonstra a existência de um preço ótimo de venda da unidade imobiliária, nem sempre conhecido pelo incorporador, e sua relação com a volatilidade do resultado do empreendimento. A metodologia demonstra que a maximização do resultado pode não coincidir com o melhor cenário de risco para o investidor. The question of how much an investor is willing to pay for a land is part of an economicfinancial study of a potential real estate venture in that location, which is traditionally analyzed by its net present value (NPV) and internal rate of return (IRR). However, in these methods of analysis, investors are not given an accurate notion of the volatility of their return on possible changes of plans by the developer and changes in the market that may occur between the purchase of the land and the sale of the real estate units. This work was proposed to look at the investment in the development of a real estate project taking into consideration the value of the option to develop the project in a land after its acquisition. The goal was to show that when considering, in the financial viability analysis, the volatility of the probability of sale of real estate units, the return of the investor is not the same as predicted in a standard financial analysis and that there is an investment value for a certain risk range that the investor is willing to assume when financing the project. The value of the option for realizing a real estate project was then calculated based on the variation in the probability of sale of real estate units in a real case scenario. The results are very significant for the decision-making of the investor. The model shows that there was an option premium of almost twice the value that was paid for the land of the development, in the economic scenario studied, however, reveals that the investment that promised a rate of return of 31% pa. according to the financial viability analysis of the developer, would pay only 19% pa. The dissertation proposes a higher quality of information to the investor by delivering the upper and lower limits of this expected rate of return, with a 95% confidence interval, and also demonstrates the existence of an optimum sale price for the real estate unit, not always known by the developer, and its relation to the volatility of the project result. The methodology demonstrates that the maximization of the result may not coincide with the best risk scenario for the investor.

En esta investigación se analiza la importancia del uso del modelo de opciones reales en la industria de autopartes mediante una aplicación del modelo al caso de una inversión directa en el exterior, específicamente en Brasil. Se utilizaron los modelos Black y Scholes y el Binomial; los resultados obtenidos muestran que este es el tipo de proyectos que, a pesar de tener un VPN negativo, deben ser aceptados a causa de su valor estratégico, lo que estaría indicando que el efecto contingente de los proyectos de inversión, traducidos en la volatilidad de los flujos de efectivo, son mejor valorados por el modelo de opciones reales ya que a diferencia del VPN este sí los considera en su valoración. This study examines the importance of using real options model in the auto industry by means of its application to the case of a direct investment abroad, specifically in Brazil. We use the Black and Scholes and Binomial models. Empirical results show that this is the kind of project that, despite having a negative NPV, should be accepted because of its strategic value, which indicates that the contingent effect of the investment projects, reflected in the volatility of cash flows, are best assessed by the real options model unlike the VPN that does not take them into account. 127-156 maluisasaavedra@yahoo.com jsaavedra2000@unsis.edu.mx deyanirabernaldominguez@gmail.com semestral

In this thesis we study some portfolio optimization and option pricing problems in market models where the dynamics of one or more risky assets are driven by Lévy processes, and it is divided in four independent parts. In the first part we study the portfolio optimization problem, for the logarithmic terminal utility and the logarithmic consumption utility, in a multi-defaultable Lévy driven model. In the second part we introduce a novel technique to price European defaultable claims when the pre-defaultable dynamics of the underlying asset follows an exponential Lévy process. In the third part we develop a novel methodology to obtain analytical expansions for the prices of European derivatives, under stochastic and/or local volatility models driven by Lévy processes, by analytically expanding the integro-differential operator associated to the pricing problem. In the fourth part we present an extension of the latter technique which allows for obtaining analytical expansion in option pricing when dealing with path-dependent Asian-style derivatives.

We recall here the basics of the most classic result of option pricing, perhaps the most famous result in mathematical finance: the Black–Scholes theory for the pricing of “European options” in a perfect market, infinitely divisible and liquid, with no “friction” such as transaction costs or information lag. However, in keeping with the spirit of this volume, we derive it via a game-theoretic approach, devoid of any probabilities.

In this paper we present two methods for the pricing of Target Volatility Options (TVOs), a recent market innovation in the field of volatility derivative. TVOs allow investors to take a joint view on the future price of a given underlying (e.g. stocks, commodities, etc) and its realized volatility. For example, a target volatility call pays at maturity the terminal value of the asset minus the strike, floored at zero, scaled by the ratio of the target volatility (an arbitrary constant) and the realized volatility of the underlying over the life of the option. TVOs are popular with investors and hedgers because they are typically cheaper than their vanilla equivalent. We present two approaches for the pricing of TVOs: a power series expansion and a Laplace transform method. We also provide both model dependent and model independent solutions. The pricing methodologies have been tested numerically and results are provided.

Les actifs financiers dérivés (swaps, futures, options, CDS, CDO, etc.) sont au coeur de la finance moderne. Instruments de protection contre le risque ou la spéculation, leur bonne utilisation nécessite une évaluation préalable minutieuse, notamment lorsque ces actifs ne sont pas cotés sur un marché. L'évaluation par arbitrage, développée à partir des principes de Black, Scholes et Merton, constitue la méthode la plus efficiente pour relever ce défi. Sa mise en oeuvre peut se faire par les modèles en temps discret ou en temps continu. Cet ouvrage présente une analyse détaillée de l'évaluation sous l'hypothèse de marchés complets. Une ouverture sur les perspectives les plus récentes de la finance comme la volatilité stochastique ou les processus à sauts est également proposée. Evaluation par arbitrage des actifs financiers concilie, par une démarche originale, rigueur et appel à l'intuition. Il s'adresse aux étudiants de mastère, de grandes écoles et aux professionnels désirant approfondir leurs connaissances des actifs financiers dérivés.

O presente estudo verificou, para o período de julho de 1994 a junho de 1997, o ajustamento ao mercado brasileiro de dois modelos de precificação de opções de compra: o de Black e Scholes (1973), que reconhece que os retornos dos preços da ação-objeto seguem um processo de difusão log-normal e o proposto por Cox e Ross (1976), que admite um processo de difusão com elasticidade da variância constante. Com a utilização de diferenças percentuais relativas e do teste t, observou-se que ambos os modelos subprecificaram opções fora do preço e no preço, enquanto, para opções dentro do preço, somente as mais próximas do vencimento foram subprecificadas. Verificou-se que o modelo de Black e Scholes (1973) ajustou-se melhor às opções fora do preço e no preço, enquanto o modelo da elasticidade da variância constante ajustou-se melhor às opções dentro do preço. Por fim, os resultados sugerem que, embora o modelo de Black e Scholes (1973) se ajuste ligeiramente melhor ao mercado brasileiro, de uma forma geral, não se pode afirmar que um modelo seja superior ao outro na precificação de opções de compra. This study examined, from July 1994 to June 1997, the goodness of fitting to the Brazilian market of two call option pricing models: the Black and Scholes (1973), which assumes that the returns of the underlying stock prices follow a lognormal diffusion process, and the constant elasticity of variance, suggested by Cox and Ross (1976), which assumes that the returns of the underlying stock prices follow a constant elasticity of variance diffusion process. Through the use of relative percentage differences and the t-test, it was verified that both models underpriced options out of the money and in the money whereas for at the money options, only the closest to the expiration day were underpriced. It was also verified that the Black and Scholes (1973) model adjusted better to out of the money and at the money options whereas the constant elasticity of variance model fitted better to in the money options. Finally, the results suggest that, although the Black and Scholes (1973) model performs slightly better than the other, it cannot be said that one model fits better to the market than the other in the pricing of Brazilian call options.

Este trabajo tiene por objeto analizar la ecuación diferencial de Black and Scholes y evaluar su aplicación en la valoración de opciones de intercambio de activos reales. Los modelos de valoración de opciones financieras, que han sido objeto de un gran desarrollo formal en los últimos años, tienen un campo de aplicación de gran interés en la valoración de activos, tanto reales (fusiones y adquisiciones de empresas, opciones de abandono y crecimiento de las inversiones, etc.) como financieros (deuda empresarial, derechos de suscripción, obligaciones convertibles, etc.) que adquieren una nueva perspectiva desde esta teoría de derechos contingentes, que complementa y, en ocasiones, sustituye con ventaja a las valoraciones tradicionales basadas en los descuentos de flujos de caja ajustados al riesgo.

Purpose: The aim of the paper is to investigate the Black and Scholes model by providing an updated framework of the international literature on the topic, within the field of real option. The purpose of the research is to identify the relevant literature between 1999 and 2015, together with the most important perspectives on the Black and Scholes model as analysed by scholars, in order to provide a useful support to the academic community in their studies. The investigation was carried out only for its economic and corporate insights, with the objective of establishing the strong and weak points highlighted in the defined framework. Methodology: The method used for the research was based on qualitative approach. International literature on the topic was examined through a research protocol. The research was developed by the identification of four keywords (Real Options Valuation, Real Options Assessment, Black and Scholes, Real Options Pricing) and searching them in two databases, with the purpose of obtaining a wide range of scientific contribution for the analysis. Originality/value: The paper presents an accurate review of the scientific contribution on the topic of the Black and Scholes model; it defines the fields of application, opportunities offered and issues relating to its application, in order to clarify the strong and weak points of the model. Practical implications: The Black and Scholes model of the 1970s is acknowledged to be the most widely used model for evaluating options. Our study shows that this method has been adopted by decision-makers not only for evaluating options but also in other fields.