Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Depression and 'crises of meaninglessness' in the political-economic theology of the money-God

The thesis starts with a historical analysis of the development of depression as a concept. Through this inquiry, the controversies behind the apparent consensus about depression’s etiology and treatment are illuminated, suggesting that the understanding of the climbing rates of depression in contemporary Western civilization is still up for grabs. That’s what the thesis sets out to investigate. In order to accomplish this aim, the study builds upon the classical accounts of Georg Simmel, Émile Durkheim and the more contemporary ideas of Dany-Robert Dufour, in dialogue with an array of supplementary theoretical sources. Navigating through this ‘sea’ of extraordinary and different theories, a new avenue of reflections arises, contributing for the sophistication of the questions made about the phenomenon of depression’s rates. The fundamental argument emerging from this theoretical undertaking is that ‘crises of meaninglessness’ that pervade the collective body of Western contemporary societies have, as one of its consequences, the expansion of depression rates. Meaninglessness in contemporary times is the primary object of investigation of the thesis. The concept, in the context of this study, is not understood as merely an effect of the historical decline of shared social norms due to processes of individualization. Rather, it is claimed, it originates from and is reinforced by the ‘political-economic theology of neo-liberalism’ which becomes virtually generalized in the West, erecting money as a God. The study concludes that by undermining culturally established values, ideals, institutions and principles that may block the dissemination of commodities this new transcendence has been challenging the task of signifying life, potentializing – among other subjective difficulties – the diffusion of depression.