A stochastic dynamic programming approach for pricing options on stock-index futures

The aim of this thesis is to price options on equity index futures with an application to standard options on S&P 500 futures traded on the Chicago Mercantile Exchange. Our methodology is based on stochastic dynamic programming, which can accommodate European as well as American options. The model accommodates dividends from the underlying asset. It also captures the optimal exercise strategy and the fair value of the option. This approach is an alternative to available numerical pricing methods such as binomial trees, finite differences, and ad-hoc numerical approximation techniques. Our numerical and empirical investigations demonstrate convergence, robustness, and efficiency. We use this methodology to value exchange-listed options. The European option premiums thus obtained are compared to Black's closed-form formula. They are accurate to four digits. The American option premiums also have a similar level of accuracy compared to premiums obtained using finite differences and binomial trees with a large number of time steps. The proposed model accounts for deterministic, seasonally varying dividend yield. In pricing futures options, we discover that what matters is the sum of the dividend yields over the life of the futures contract and not their distribution.

Optimal and Long-Term Dynamic Transport Policy Design: Seeking Maximum Social Welfare through a Pricing Scheme.

This article presents an alternative approach to the decision-making process in transport strategy design. The study explores the possibility of integrating forecasting, assessment and optimization procedures in support of a decision-making process designed to reach the best achievable scenario through mobility policies. Long-term evaluation, as required by a dynamic system such as a city, is provided by a strategic Land-Use and Transport Interaction (LUTI) model. The social welfare achieved by implementing mobility LUTI model policies is measured through a cost-benefit analysis and maximized through an optimization process throughout the evaluation period. The method is tested by optimizing a pricing policy scheme in Madrid on a cordon toll in a context requiring system efficiency, social equity and environmental quality. The optimized scheme yields an appreciable increase in social surplus through a relatively low rate compared to other similar pricing toll schemes. The results highlight the different considerations regarding mobility impacts on the case study area, as well as the major contributors to social welfare surplus. This leads the authors to reconsider the cost-analysis approach, as defined in the study, as the best option for formulating sustainability measures.

Optimal and Long-Term Dynamic Transport Policy Design: Seeking Maximum Social Welfare through a Pricing Scheme

This article presents an alternative approach to the decision-making process in transport strategy design. The study explores the possibility of integrating forecasting, assessment and optimization procedures in support of a decision-making process designed to reach the best achievable scenario through mobility policies. Long-term evaluation, as required by a dynamic system such as a city, is provided by a strategic Land-Use and Transport Interaction (LUTI) model. The social welfare achieved by implementing mobility LUTI model policies is measured through a cost-benefit analysis and maximized through an optimization process throughout the evaluation period. The method is tested by optimizing a pricing policy scheme in Madrid on a cordon toll in a context requiring system efficiency, social equity and environmental quality. The optimized scheme yields an appreciable increase in social surplus through a relatively low rate compared to other similar pricing toll schemes. The results highlight the different considerations regarding mobility impacts on the case study area, as well as the major contributors to social welfare surplus. This leads the authors to reconsider the cost-analysis approach, as defined in the study, as the best option for formulating sustainability measures.

Scenario Planning and Evaluation of Pricing Strategies in the Portuguese Bulk LPG Market

Portugal has the largest LPG (Liquefied Petroleum Gas) share of primary energy demand in the EU (about 5%). Due to the increasing international cost of LPG in the last years and the high price sensitivity of the consumers the preference for substitute energy sources in new and existing consumers has been increasing. To select the kind of energy, some consumer estimate and compare the total costs while others follow agents (equipment sellers) recommendations. It takes time to build agents perception about the most advantageous source of energy, which is seen as an important resource that drives client resource accumulation and retention. Marketing strategies have to take into consideration some market dynamic effects derived from the accumulation and depletion of these resources. A simple system dynamics model was built, combined with Economic Value Added framework, to evaluate some pricing strategies under different scenarios of LPG international cost.

Scenario Planning and Evaluation of Pricing Strategies in the Portuguese Bulk LPG Market

Portugal has the largest LPG (Liquefied Petroleum Gas) share of primary energy demand in the EU (about 5%). Due to the increasing international cost of LPG in the last years and the high price sensitivity of the consumers the preference for substitute energy sources in new and existing consumers has been increasing. To select the kind of energy, some consumer estimate and compare the total costs while others follow agents (equipment sellers) recommendations. It takes time to build agents perception about the most advantageous source of energy, which is seen as an important resource that drives client resource accumulation and retention. Marketing strategies have to take into consideration some market dynamic effects derived from the accumulation and depletion of these resources. A simple system dynamics model was built, combined with Economic Value Added framework, to evaluate some pricing strategies under different scenarios of LPG international cost.

Memória de longo prazo nos retornos acionistas dos índices de referência da euronext, implicações para a hipótese de mercados eficientes e contributo fractal para aperfeiçoamento do capital asset pricing model

Não existe uma definição única de processo de memória de longo prazo. Esse processo é geralmente definido como uma série que possui um correlograma decaindo lentamente ou um espectro infinito de frequência zero. Também se refere que uma série com tal propriedade é caracterizada pela dependência a longo prazo e por não periódicos ciclos longos, ou que essa característica descreve a estrutura de correlação de uma série de longos desfasamentos ou que é convencionalmente expressa em termos do declínio da lei-potência da função auto-covariância. O interesse crescente da investigação internacional no aprofundamento do tema é justificado pela procura de um melhor entendimento da natureza dinâmica das séries temporais dos preços dos ativos financeiros. Em primeiro lugar, a falta de consistência entre os resultados reclama novos estudos e a utilização de várias metodologias complementares. Em segundo lugar, a confirmação de processos de memória longa tem implicações relevantes ao nível da (1) modelação teórica e econométrica (i.e., dos modelos martingale de preços e das regras técnicas de negociação), (2) dos testes estatísticos aos modelos de equilíbrio e avaliação, (3) das decisões ótimas de consumo / poupança e de portefólio e (4) da medição de eficiência e racionalidade. Em terceiro lugar, ainda permanecem questões científicas empíricas sobre a identificação do modelo geral teórico de mercado mais adequado para modelar a difusão das séries. Em quarto lugar, aos reguladores e gestores de risco importa saber se existem mercados persistentes e, por isso, ineficientes, que, portanto, possam produzir retornos anormais. O objetivo do trabalho de investigação da dissertação é duplo. Por um lado, pretende proporcionar conhecimento adicional para o debate da memória de longo prazo, debruçando-se sobre o comportamento das séries diárias de retornos dos principais índices acionistas da EURONEXT. Por outro lado, pretende contribuir para o aperfeiçoamento do capital asset pricing model CAPM, considerando uma medida de risco alternativa capaz de ultrapassar os constrangimentos da hipótese de mercado eficiente EMH na presença de séries financeiras com processos sem incrementos independentes e identicamente distribuídos (i.i.d.). O estudo empírico indica a possibilidade de utilização alternativa das obrigações do tesouro (OT’s) com maturidade de longo prazo no cálculo dos retornos do mercado, dado que o seu comportamento nos mercados de dívida soberana reflete a confiança dos investidores nas condições financeiras dos Estados e mede a forma como avaliam as respetiva economias com base no desempenho da generalidade dos seus ativos. Embora o modelo de difusão de preços definido pelo movimento Browniano geométrico gBm alegue proporcionar um bom ajustamento das séries temporais financeiras, os seus pressupostos de normalidade, estacionariedade e independência das inovações residuais são adulterados pelos dados empíricos analisados. Por isso, na procura de evidências sobre a propriedade de memória longa nos mercados recorre-se à rescaled-range analysis R/S e à detrended fluctuation analysis DFA, sob abordagem do movimento Browniano fracionário fBm, para estimar o expoente Hurst H em relação às séries de dados completas e para calcular o expoente Hurst “local” H t em janelas móveis. Complementarmente, são realizados testes estatísticos de hipóteses através do rescaled-range tests R/S , do modified rescaled-range test M - R/S e do fractional differencing test GPH. Em termos de uma conclusão única a partir de todos os métodos sobre a natureza da dependência para o mercado acionista em geral, os resultados empíricos são inconclusivos. Isso quer dizer que o grau de memória de longo prazo e, assim, qualquer classificação, depende de cada mercado particular. No entanto, os resultados gerais maioritariamente positivos suportam a presença de memória longa, sob a forma de persistência, nos retornos acionistas da Bélgica, Holanda e Portugal. Isto sugere que estes mercados estão mais sujeitos a maior previsibilidade (“efeito José”), mas também a tendências que podem ser inesperadamente interrompidas por descontinuidades (“efeito Noé”), e, por isso, tendem a ser mais arriscados para negociar. Apesar da evidência de dinâmica fractal ter suporte estatístico fraco, em sintonia com a maior parte dos estudos internacionais, refuta a hipótese de passeio aleatório com incrementos i.i.d., que é a base da EMH na sua forma fraca. Atendendo a isso, propõem-se contributos para aperfeiçoamento do CAPM, através da proposta de uma nova fractal capital market line FCML e de uma nova fractal security market line FSML. A nova proposta sugere que o elemento de risco (para o mercado e para um ativo) seja dado pelo expoente H de Hurst para desfasamentos de longo prazo dos retornos acionistas. O expoente H mede o grau de memória de longo prazo nos índices acionistas, quer quando as séries de retornos seguem um processo i.i.d. não correlacionado, descrito pelo gBm(em que H = 0,5 , confirmando- se a EMH e adequando-se o CAPM), quer quando seguem um processo com dependência estatística, descrito pelo fBm(em que H é diferente de 0,5, rejeitando-se a EMH e desadequando-se o CAPM). A vantagem da FCML e da FSML é que a medida de memória de longo prazo, definida por H, é a referência adequada para traduzir o risco em modelos que possam ser aplicados a séries de dados que sigam processos i.i.d. e processos com dependência não linear. Então, estas formulações contemplam a EMH como um caso particular possível.

DYNAMOD – A dynamic agent based modelling framework for digital businesses

Digital Businesses have become a major driver for economic growth and have seen an explosion of new startups. At the same time, it also includes mature enterprises that have become global giants in a relatively short period of time. Digital Businesses have unique characteristics that make the running and management of a Digital Business much different from traditional offline businesses. Digital businesses respond to online users who are highly interconnected and networked. This enables a rapid flow of word of mouth, at a pace far greater than ever envisioned when dealing with traditional products and services. The relatively low cost of incremental user addition has led to a variety of innovation in pricing of digital products, including various forms of free and freemium pricing models. This thesis explores the unique characteristics and complexities of Digital Businesses and its implications on the design of Digital Business Models and Revenue Models. The thesis proposes an Agent Based Modeling Framework that can be used to develop Simulation Models that simulate the complex dynamics of Digital Businesses and the user interactions between users of a digital product. Such Simulation models can be used for a variety of purposes such as simple forecasting, analysing the impact of market disturbances, analysing the impact of changes in pricing models and optimising the pricing for maximum revenue generation or a balance between growth in usage and revenue generation. These models can be developed for a mature enterprise with a large historical record of user growth rate as well as for early stage enterprises without much historical data. Through three case studies, the thesis demonstrates the applicability of the Framework and its potential applications.

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities (Draft 1)

We extend a reduced form model for pricing pass-through mortgage backed securities (MBS) and provide a novel hedging tool for investors in this market. To calculate the price of an MBS, traders use what is known as option-adjusted spread (OAS). The resulting OAS value represents the required basis points adjustment to reference curve discounting rates needed to match an observed market price. The OAS suffers from some drawbacks. For example, it remains constant until the maturity of the bond (thirty years in mortgage-backed securities), and does not incorporate interest rate volatility. We suggest instead what we call dynamic option adjusted spread (DOAS). The latter allows investors in the mortgage market to account for both prepayment risk and changes of the yield curve.

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities (Draft 2)

We extend a reduced form model for pricing pass-through mortgage backed securities (MBS) and provide a novel hedging tool for investors in this market. To calculate the price of an MBS, traders use what is known as option-adjusted spread (OAS). The resulting OAS value represents the required basis points adjustment to reference curve discounting rates needed to match an observed market price. The OAS suffers from some drawbacks. For example, it remains constant until the maturity of the bond (thirty years in mortgage-backed securities), and does not incorporate interest rate volatility. We suggest instead what we call dynamic option adjusted spread (DOAS), which allows investors in the mortgage market to account for both prepayment risk and changes of the yield curve.

A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)

Three essays in dynamic corporate finance

Summary Throughout my thesis, I elaborate on how real and financing frictions affect corporate decision making under uncertainty, and I explore how firms time their investment and financing decisions given such frictions. While the macroeconomics literature has focused on the impact of real frictions on investment decisions assuming all equity financed firms, the financial economics literature has mainly focused on the study of financing frictions. My thesis therefore assesses the join interaction of real and financing frictions in firms' dynamic investment and financing decisions. My work provides a rationale for the documented poor empirical performance of neoclassical investment models based on the joint effect of real and financing frictions on investment. A major observation relies in how the infrequency of corporate decisions may affect standard empirical tests. My thesis suggests that the book to market sorts commonly used in the empirical asset pricing literature have economic content, as they control for the lumpiness in firms' optimal investment policies. My work also elaborates on the effects of asymmetric information and strategic interaction on firms' investment and financing decisions. I study how firms time their decision to raise public equity when outside investors lack information about their future investment prospects. I derive areal-options model that predicts either cold or hot markets for new stock issues conditional on adverse selection, and I provide a rational approach to study jointly the market timing of corporate decisions and announcement effects in stock returns. My doctoral dissertation therefore contributes to our understanding of how under real and financing frictions may bias standard empirical tests, elaborates on how adverse selection may induce hot and cold markets in new issues' markets, and suggests how the underlying economic behaviour of firms may induce alternative patterns in stock prices.

On the term structure of Interbank interest rates: Jump-diffusion processes and option pricing

In this paper we study the dynamic behavior of the term structureof Interbank interest rates and the pricing of options on interest ratesensitive securities. We posit a generalized single factor model withjumps to take into account external influences in the market. Daily datais used to test for jump effects. Qualitative examination of the linkagebetween Monetary Authorities' interventions and jumps are studied. Pricingresults suggests a systematic underpricing in bonds and call options ifthe jumps component is not included. However, the pricing of put optionson bonds presents indeterminacies.