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The current world financial scene indicates at an intertwined and interdependent relationship between financial market activity and economic health. This book explains how the economic messages delivered by the dynamic evolution of financial asset returns are strongly related to option prices. The Black Scholes framework is introduced and by underlining its shortcomings, an alternative approach is presented that has emerged over the past ten years of academic research, an approach that is much more grounded on a realistic statistical analysis of data rather than on ad hoc tractable continuous time option pricing models. The reader then learns what it takes to understand and implement these option pricing models based on time series analysis in a self-contained way. The discussion covers modeling choices available to the quantitative analyst, as well as the tools to decide upon a particular model based on the historical datasets of financial returns. The reader is then guided into numerical deduction of option prices from these models and illustrations with real examples are used to reflect the accuracy of the approach using datasets of options on equity indices.
Many recent advances in modelling within the applied sciences and engineering have focused on the increasing importance of sensitivity analyses. For a given physical, financial or environmental model, increased emphasis is now placed on assessing the consequences of changes in model outputs that result from small changes or errors in both the hypotheses and parameters. The approach proposed in this book is entirely new and features two main characteristics. Even when extremely small, errors possess biases and variances. The methods presented here are able, thanks to a specific differential calculus, to provide information about the correlation between errors in different parameters of the mo...
This book combines theory and practice to analyze risk measurement from different points of view. The limitations of a model depend on the framework on which it has been built as well as specific assumptions, and risk managers need to be aware of these when assessing risks. The authors investigate the impact of these limitations, propose an alternative way of thinking that challenges traditional assumptions, and also provide novel solutions. Starting with the traditional Value at Risk (VaR) model and its limitations, the book discusses concepts like the expected shortfall, the spectral measure, the use of the spectrum, and the distortion risk measures from both a univariate and a multivariate perspective.
The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician. Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, clima...
A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: i...
The year's finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2020 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday aspects of math, and take readers behind the scenes of today’s hottest mathematical debates. Here, Steven Strog...
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Tout comme les travaux de Darwin, la révolution provoquée par la découverte de la double hélice, en 1953, tient à l'ordre de grandeur vertigineux des possibilités combinatoires. Le vivant que nous connaissons n'est qu'une infime partie de ce qui est concevable. Ces ADN qui n'existent pas, et qui pour beaucoup d'entre eux n'ont jamais existé, posent la question majeure de la rencontre fortuite de molécules artificielles avec l'existant. Cette problématique, unique dans l'histoire, interroge la notion de providence qui est en balance avec celle de précaution. Au-delà des religions, bien des scientifiques ont une vision providentielle du progrès technique. C'est le cas en biologie d...
Comment relever les extraordinaires défis que nous lancent les crises induites par la destruction de notre habitat planétaire ? Faut-il réviser le concept même de propriété privée ? Remettre en cause la souveraineté des États-nations ? Comment construire ensemble les institutions internationales qui permettraient de prendre soin de nos communs globaux que sont le climat mais aussi la biodiversité, la santé, les cultures et jusqu’à la démocratie ? Car c'est elle qui, aujourd'hui, est menacée par notre refus d'inscrire des limites à la toute-puissance de la personnalité juridique, des techniques extractivistes et de la marchandisation du monde. Où trouverons-nous les ressour...
Gaël Giraud y Cécile Renouard formulan 20 postulados controversiales para generar cambios profundos en los sistemas financieros internacionales, como solución a la crisis económica mundial; la principal consecuencia de la caída del mercado de finca raíz de los Estados Unidos en el 2008. Este libro plantea modificaciones fundamentales a los modelos económicos e invita a considerar el rol de la responsabilidad social y ambiental de las empresas y a fijar límites a la expansión de la esfera del mercado.