Valuation of European-Style swaptions

Tese de mestrado em Matemática Financeira, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2010The present work focuses on the pricing of European-style interest rate swaptions, using the Edgeworth expansion [Collin-Dufresne and Goldstein (2002)] and the Hyperplane approxima-tions [Singleton and Umantsev (2002)], under multi-factor exponentially-affine models of the term structure. In a market without arbitrage opportunities, it is shown that an interest rate swaption can be priced as an option on a coupon-bearing bond. While the Edgeworth approx-imation suggests a cumulant expansion of the probability density function of the price of the underlying coupon-bearing bond, the Hyperplane approximation proposes a linearization of the exercise region, so that the same methods used when under one-factor models can be applied. Both methods are analyzed in detailed, and then implemented considering a three-factor Gaussian model, and different maturities for the underlying interest rate swaps, as well as a range of strike prices for each swaption. While there are almost no differences between the results yielded by both approximations, the Edgeworth approximation proves to be significantly slower as the time-to-maturity of the underlying swap increases. Moreover, the Edgeworth approximation is less .flexible, because it requires a closed-form solution for the moments of the distribution of the underlying asset (i.e. a coupon-bearing bond), which are not so readily available for non-affine term structure models

The impact of acceleration programs on early-stage tech-startups considering the founders’ background

The growth of tech-startups such as Airbnb and Uber into multibillion-dollar companies has a strong impact on the economy. Yet, 50% of startups close the business within 5 years, which makes it crucial to have support organizations, such as accelerators, to mitigate these failure rates. Accelerators help new ventures with a pre-defined business support. Nonetheless, this business support will be absorbed and implemented at different speeds since founding team members usually have different areas of expertise. Thus, we aim at uncovering the benefits of acceleration programs, what drives those benefits and if the outcomes differ according to the founder’s background – considering their opposite learning types (exploitative vs exploratory). Data was collected through 14 semi-structured interviews and analyzed using inductive thematical analysis. Results suggest that most benefits are business model improvement, key project modifications and business/entrepreneurial knowledge and the drivers are time compression, networking, mentoring and training/curriculum. Concerning the differences related to their backgrounds, views on exploitative and explorative learning find echo in our results as business founders benefit more from networking and only fine-tune their business, while technical founders benefit mainly from mentoring and incur in bigger and more important changes. Further findings indicate accelerators can improve their impact by selecting participants based on their value proposition, focusing on knowledge transferring and in one sector/industry, leveling the startup's stages in each cohort and following-up after the programs. For founders, we recommend a thorough screening of accelerators before applying and a preparation before-hand to get the most value from the programs.O crescimento de startups como o Airbnb e a Uber tem um impacto comprovado na economia. No entanto, 50% das startups fecham nos primeiros 5 anos, o que dá importância a organizações de apoio como aceleradoras, que mitigam o insucesso com programas focados em gestão. Contudo, este conhecimento é absorvido a velocidades diferentes devido às diferentes áreas de conhecimento dos empreendedores. Este estudo identifica os benefícios destes programas, as causas desses benefícios e se os resultados diferem conforme o conhecimento dos fundadores – sendo que teriam aprendizagens distintas (explorativa/exploratória). Para tal, foram realizadas e analisadas 14 entrevistas. Os resultados sugerem que os benefícios mais comuns são a melhoria do modelo de negócios, mudanças estratégicas e aquisição de conhecimento empresarial/empreendedor e que os condutores dos benefícios são a limitação temporal, os contactos obtidos, a mentoria e o currículo. A ligação entre o conhecimento dos fundadores e uma aprendizagem exploratória e explorativa está espelhada nos resultados. Os fundadores de gestão beneficiam mais dos contactos obtidos e são mais propensos a melhorar o modelo de negócios, enquanto os fundadores técnicos beneficiam principalmente da mentoria e fazem mais mudanças estratégicas. Outros resultados indicam que as aceleradoras podem melhorar o seu impacto se selecionarem fundadores de acordo com a proposta de valor, focarem na transferência de conhecimento e num sector/industria, nivelarem o estado das startups em cada edição e fizerem follow-up. Para os fundadores, as recomendações são que façam uma triagem das aceleradoras antes da candidatara e preparação prévia para poderem retirar mais valor dos programas

A practical comparison between two powerful PCC codec’s

Recent advances in the consumption of 3D content creates the necessity of efficient ways to visualize and transmit 3D content. As a result, methods to obtain that same content have been evolving, leading to the development of new methods of representations, namely point clouds and light fields. A point cloud represents a set of points with associated Cartesian coordinates associated with each point(x, y, z), as well as being able to contain even more information inside that point (color, material, texture, etc). This kind of representation changes the way on how 3D content in consumed, having a wide range of applications, from videogaming to medical ones. However, since this type of data carries so much information within itself, they are data-heavy, making the storage and transmission of content a daunting task. To resolve this issue, MPEG created a point cloud coding normalization project, giving birth to V-PCC (Video-based Point Cloud Coding) and G-PCC (Geometry-based Point Cloud Coding) for static content. Firstly, a general analysis of point clouds is made, spanning from their possible solutions, to their acquisition. Secondly, point cloud codecs are studied, namely VPCC and G-PCC from MPEG. Then, a state of art study of quality evaluation is performed, namely subjective and objective evaluation. Finally, a report on the JPEG Pleno Point Cloud, in which an active colaboration took place, is made, with the comparative results of the two codecs and used metrics.Os avanços recentes no consumo de conteúdo 3D vêm criar a necessidade de maneiras eficientes de visualizar e transmitir conteúdo 3D. Consequentemente, os métodos de obtenção desse mesmo conteúdo têm vindo a evoluir, levando ao desenvolvimento de novas maneiras de representação, nomeadamente point clouds e lightfields. Um point cloud (núvem de pontos) representa um conjunto de pontos com coordenadas cartesianas associadas a cada ponto (x, y, z), além de poder conter mais informação dentro do mesmo (cor, material, textura, etc). Este tipo de representação abre uma nova janela na maneira como se consome conteúdo 3D, tendo um elevado leque de aplicações, desde videojogos e realidade virtual a aplicações médicas. No entanto, este tipo de dados, ao carregarem com eles tanta informação, tornam-se incrivelmente pesados, tornando o seu armazenamento e transmissão uma tarefa hercúleana. Tendo isto em mente, a MPEG criou um projecto de normalização de codificação de point clouds, dando origem ao V-PCC (Video-based Point Cloud Coding) e G-PCC (Geometry-based Point Cloud Coding) para conteúdo estático. Esta dissertação tem como objectivo uma análise geral sobre os point clouds, indo desde as suas possívei utilizações à sua aquisição. Seguidamente, é efectuado um estudo dos codificadores de point clouds, nomeadamente o V-PCC e o G-PCC da MPEG, o estado da arte da avaliação de qualidade, objectiva e subjectiva, e finalmente, são reportadas as actividades da JPEG Pleno Point Cloud, na qual se teve uma colaboração activa

Essays on option pricing, with applications on interest rates, equities and credit derivatives

JEL Classification: G13This thesis is devoted to option pricing, with applications on interest rates, equities and credit derivatives, and is comprised of three separate and self-contained essays: A Pricing Swaptions under Multifactor Gaussian HJM Models Several approximations have been proposed in the literature for the pricing of European-style swaptions under multifactor term structure models. However, none of them provides an estimate for the inherent approximation error. Until now, only the Edgeworth expansion technique of Collin-Dufresne and Goldstein (2002) is able to characterize the order of the approximation error. Under a multifactor Heath, Jarrow, and Morton (1992) Gaussian framework, this paper proposes a new approximation for European-style swaptions, which is able to set bounds on the magnitude of the approximation error and is based on the conditioning approach initiated by Curran (1994) and Rogers and Shi (1995). All the proposed pricing bounds will arise as a simple by-product of the Nielsen and Sandmann (2002) setup, and will be shown to provide a better accuracy-efficiency trade-off than all the approximations already proposed in the literature. B Pricing of European-style Barrier Options under Stochastic Interest Rates This paper offers an extremely fast and accurate novel methodology for the pricing of (long-term) European-style single barrier options on underlying spot prices driven by a geometric Brownian motion and under the stochastic interest rates framework of Vasiček (1977). The proposed valuation methodology extends the stopping time approach of Kuan and Webber (2003) to a more general setting, and expresses the price of a European-style barrier option in terms of the first passage time density of the underlying asset price to the barrier level. Using several model parameter constellations and option maturities, our numerical results show that the proposed pricing approach is much more accurate and faster than the two-dimensional extended Fortet method of Bernard et al. (2008). C Pricing Credit and Equity Default Swaps under the Jump to Default Extended CEV Model This paper offers a novel methodology for the pricing of credit and equity default swaps under the jump to default extended constant elasticity of variance (JDCEV) model of Carr and Linetsky (2006). The proposed method extends the stopping time approach of Kuan and Webber (2003), and expresses the value of the building blocks of both contracts in terms of the first passage time density of the underlying asset price to the contract triggering level. The numerical results show that the proposed pricing methodology is extremely accurate and much faster than the Laplace transform approach of Mendoza-Arriaga and Linetsky (2011).Esta tese dedica-se ao tema da avaliação de opções, com aplicações a taxas de juro, ações e derivados de crédito, e é composta por três artigos distintos: A Pricing Swaptions under Multifactor Gaussian HJM Models Várias aproximações foram já propostas na literatura para a avaliação de swaptions de estilo Europeu, no âmbito de modelos de taxa de juro multi-fator. Contudo, nenhuma delas fornece uma estimativa para o erro de aproximação subjacente. Até agora, apenas a Edgeworth expansion technique de Collin-Dufresne e Goldstein (2002) é capaz de caracterizar a ordem do erro de aproximação. No âmbito de um modelo Heath, Jarrow e Morton (1992) Gaussiano multi-fator, este artigo propõe uma nova aproximação para swaptions de estilo Europeu, que é capaz de estabelecer limites para a magnitude do erro de aproximação e é baseada na conditioning approach iniciada por Curran (1994) e Rogers e Shi (1995). Todos os limites de preço propostos surgirão como um simples sub-produto da estrutura de Nielsen e Sandmann (2002), e será demonstrado que estes proporcionam um melhor equilíbrio entre precisão e eficiência do que todas as aproximações já propostas na literatura. B Pricing of European-style Barrier Options under Stochastic Interest Rates Este artigo oferece uma nova metodologia, extremamente rápida e precisa, para a avaliação de opções de estilo Europeu com barreira sobre ativos subjacentes caracterizados por um geometric Brownian motion e no âmbito do modelo de taxas de juro estocásticas de Vasiček (1977). A metodologia de avaliação proposta estende a stopping time approach de Kuan e Webber (2003) a uma configuração mais geral, e expressa o preço de uma opção de estilo Europeu com barreira em termos da densidade de probabilidade do primeiro tempo de passagem do preço do ativo subjacente pelo nível da barreira. Utilizando várias configurações de parâmetros e maturidades de opções, os nossos resultados numéricos mostram que a metodologia de avaliação proposta é muito mais precisa e rápida do extended Fortet method bi-dimensional de Bernard et al. (2008). C Pricing Credit and Equity Default Swaps under the Jump to Default Extended CEV Model Este artigo oferece uma nova metodologia para a avaliação de credit e equity default swaps no âmbito do modelo jump to default extended constant elasticity of variance (JDCEV) de Carr e Linetsky (2006). A abordagem proposta estende a stopping time approach de Kuan e Webber (2003), e expressa o valor das componentes de ambos os contratos em termos da densidade de probabilidade do primeiro tempo de passagem do preço do ativo subjacente pelo nível de acionamento do contrato. Os resultados numéricos mostram que a abordagem de avaliação proposta é precisa e muito mais rápida do que a Laplace transform approach de Mendoza-Arriaga e Linetsky (2011)

COVID-19 or threat of a nuclear war in Europe? A cross-sectional study of anxiety levels in adults living in Portugal

BackgroundSince 2019, Europe has experienced ongoing stressors with the emergence of the COVID-19 pandemic and the Russian–Ukrainian War, which have had social, financial, physical, and psychological impacts. Studies suggest that anxiety, fear, post-traumatic stress disorder, depression, and other psychological disorders are common in such situations, and there is a need for more research on the impact of the war on mental health in Portugal. The main goal of the present study was to assess the impact of the fear of COVID-19 and anxiety related to nuclear war on the general anxiety levels of adult individuals living in Portugal.MethodsA cross-sectional study was conducted from May to July 2022 using an online questionnaire built on the Google Forms platform. Portuguese-speaking male and female individuals aged 18 years or older, who provided informed consent and agreed to participate, were included. The outcome variable was defined using the Portuguese version of the GAD-7 scale, while the main predictors were the FCV-19S and the NWA Scale in Portuguese. Linear and logistic regression models were used to test associations between predictors and outcome variable.ResultsThe study included 1,182 participants, with a mean age of 46.5 (±11.7) years, mostly women (80.6%). The global mean GAD-7 score was 5.8 (±4.5) points, and 17.9% of the participants scored above the 10-point cutoff. Higher scores were found in both the FCV-19S and the NWA scale among participants with anxiety, as measured by both a 10-point cutoff (p < 0.001), and GAD-7 scale mean scores (p < 0.001). The study showed that fear of COVID-19 [OR of 1.133 (95%CI: 1.097–1.170)] and, at a lesser extent, nuclear war anxiety [OR of 1.020 (95%CI, 1.009–1.031)] contribute to anxiety in the general population. This is also true for those with a personal history of anxiety, revealed by multiple regression.DiscussionThis study contributes to the research on COVID-19’s impact on anxiety and provides the first comprehensive assessment of nuclear war anxiety in Portugal. Results highlight the need for long-term care for anxiety, as prevalence is expected to increase due to the pandemic and war, even in non-conflict areas like Portugal

Equilibration of Isolated Systems: investigating the role of coarse-graining on the initial state magnetization

Many theoretical and experimental results show that even isolated quantum systems evolving unitarily may equilibrate, since the evolution of some observables may be around an equilibrium value with negligible fluctuations most of the time. There are rigorous theorems giving the conditions for such equilibration to happen. In particular, initial states prepared with a lack of resolution in the energy will equilibrate. We investigate how equilibration may be affected by a lack of resolution, or coarse-graining, in the magnetization of the initial state. In particular, for a chaotic spin chain and using exact diagonalization, we show that an initial state with a coarse, not well-defined magnetization in the z direction show a greater tendency to equilibrate when compared with an initial state with well-defined magnetization. And this tendency will depend on the degree of coarse-graining. We also analyze the time for the system to reach equilibrium, showing good agreement with theoretical estimates and with some evidence that less resolution leads to faster equilibration. Our study highlights the crucial role of initial state preparation in the equilibration dynamics of quantum systems and provides new insights into the fundamental nature of equilibration in closed systems

COVID-19 or threat of a nuclear war in Europe? A cross-sectional study of anxiety levels in adults living in Portugal

Background: Since 2019, Europe has experienced ongoing stressors with the emergence of the COVID-19 pandemic and the Russian–Ukrainian War, which have had social, financial, physical, and psychological impacts. Studies suggest that anxiety, fear, post-traumatic stress disorder, depression, and other psychological disorders are common in such situations, and there is a need for more research on the impact of the war on mental health in Portugal. The main goal of the present study was to assess the impact of the fear of COVID-19 and anxiety related to nuclear war on the general anxiety levels of adult individuals living in Portugal. Methods: A cross-sectional study was conducted from May to July 2022 using an online questionnaire built on the Google Forms platform. Portuguese-speaking male and female individuals aged 18 years or older, who provided informed consent and agreed to participate, were included. The outcome variable was defined using the Portuguese version of the GAD-7 scale, while the main predictors were the FCV-19S and the NWA Scale in Portuguese. Linear and logistic regression models were used to test associations between predictors and outcome variable. Results: The study included 1,182 participants, with a mean age of 46.5 (±11.7) years, mostly women (80.6%). The global mean GAD-7 score was 5.8 (±4.5) points, and 17.9% of the participants scored above the 10-point cutoff. Higher scores were found in both the FCV-19S and the NWA scale among participants with anxiety, as measured by both a 10-point cutoff (p < 0.001), and GAD-7 scale mean scores (p < 0.001). The study showed that fear of COVID-19 [OR of 1.133 (95%CI: 1.097–1.170)] and, at a lesser extent, nuclear war anxiety [OR of 1.020 (95%CI, 1.009–1.031)] contribute to anxiety in the general population. This is also true for those with a personal history of anxiety, revealed by multiple regression. Discussion: This study contributes to the research on COVID-19’s impact on anxiety and provides the first comprehensive assessment of nuclear war anxiety in Portugal. Results highlight the need for long-term care for anxiety, as prevalence is expected to increase due to the pandemic and war, even in non-conflict areas like Portugal.info:eu-repo/semantics/publishedVersio

Pickering Emulsions Stabilized by Calcium Carbonate Particles: A New Topical Formulation

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Pickering emulsions are systems composed of two immiscible fluids stabilized by solid organic or inorganic particles. Pickering emulsions are particularly useful in cosmetics, where the surfactants are unwanted, as well as in the pharmaceutical field, where transdermal and/or dermal drug delivery is difficult to achieve and controlled drug release is desired. Here, we studied calcium carbonate particles as stabilizers of Pickering emulsions for topical use. An optimized formulation was obtained using a Quality by Design approach. First, a screening experiment was performed to identify the formulation and process critical variables that affect the quality properties of the Pickering emulsion. The optimization of the production was then studied by establishing the design space. The final formulation was hereinafter investigated regarding the pH, rheological properties, and in vitro cytotoxicity assays. The results showed the formulation had a pH compatible with human skin and a shear thinning behavior. Moreover, this formulation showed a strong network structure, with a suitable spreadability on the skin, allowing an easy application. The in vitro assays were performed to assess the potential cytotoxicity of the calcium carbonate-stabilized emulsion and the particles themselves, and the results revealed that the formulation did not significantly affect the cell viability. In conclusion, the use of calcium carbonate particles as a stabilizer ingredient contributed to achieve an eco-friendly Pickering emulsion.This research was funded by Fundação para a Ciência e a Tecnologia, Portugal (UID/DTP/04138/2019, PTDC/MEC-DER/30198/2017, and CEECINST/00145/2018) and by Carbomin.info:eu-repo/semantics/publishedVersio

Physician empathy and patient enablement: survey in the Portuguese primary health care

Background: Empathy is the capacity to understand and resonate with the experiences of other people. Patient enablement is the degree to which a patient feels strengthened in terms of being able to deal with, understand and manage their disease. Methods: Secondary cross-sectional analysis of existing data from 2 independent datasets (456 primary health care patients), with the application of two validated questionnaires, Jefferson Scale of Patient Perceptions of Physician Empathy (JSPPPE) and Patient Enablement Instrument (PEI). Objective: Evaluate medical empathy and patients’ enablement after consultation with their family doctors and to verify if there was an association between these two concepts. Results: The median value of JSPPPE-VP score was 6.60 (interquartile range 1.00) and of PEI/ICC score was of 1.83 (interquartile range 0.67). Regarding empathy (JSPPPE-VP), patients taking chronic medication had a slight but significantly higher median score than patients not taking them (6.70 versus 6.60, P = 0.049), although regression modelling did not confirm any relevant predictor of JSPPPE-VP score. Regarding enablement (PEI/ICC), we found significantly higher scores on younger patients, as well as, on more educated and professionally active ones (P < 0.001). Multivariable linear regression and Poisson regression modelling confirmed such variables as statistically significant potential predictors. Conclusions: A significant positive association was found between empathy score (JSPPPE-VP) and enablement score (PEI/ICC), when adjusted to sociodemographic cofactors. On this linear regression model, age category and educational level were also significantly associated with empathy score, with the same pattern found on bivariate analysis.info:eu-repo/semantics/publishedVersio