Renewal equations for option pricing

In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined

Are there evidences of a complex mimicry system among Asclepias curassavica (Apocynaceae), Epidendrum fulgens (Orchidaceae), and Lantana camara (Verbenaceae) in Southern Brazil?

The goal of this paper was to test the presence of mimicry in Asclepias curassavica L., Epidendrum fulgens Brong., and Lantana camara L. The study was carried out at the Parque Estadual de Itapeva, RS, southern Brazil, from 2004 to 2006. Flowering period of each of the three species was followed up; focal observations of butterflies visiting flowers, from fixed point and during random walks were carried out. We also estimated the frequency of pollinaria removal in the orchid, as well as its mode of reproduction. All these variables were important for testing the mimicry hypothesis. Despite some temporal coincidences in the flowering period of two plants in the system, there was no statistical association among the three plants as to flowering period. Twenty-nine species of butterflies, as potential pollinators, were recorded, particularly Agraulis vanillae maculosa, Dryas iulia alcionea, Urbanus simplicius, Tegosa claudina, and Heliconius erato phyllis, which were the more frequent visitors of the three plants. There was association between the number of visits to L. camara and E. fulgens, based on Pearson correlation (r = 0.4603; n = 19; P = 0.0473). Pollinaria removal of E. fulgens was low, as measured by the percentage of removal (range: 0 - 10%). The analysis of the mode of reproduction of this orchid showed its pollinator-dependence, since no fruits were formed by spontaneous self-pollination. In contrast, the percentage of fruit set that resulted from geitonogamy and xenogamy was, in average, 86%. The results here shown are not conclusive as to the occurrence of a mimicry system among the three plants.

Temps de Branchement du Mouvement Brownien Branchant Inhomogène

Ce mémoire étudie le comportement des particules dont la position est maximale au temps t dans la marche aléatoire branchante et le mouvement brownien branchant sur R, pour des valeurs de t grandes. Plus exactement, on regarde le comportement du maximum d’une marche aléatoire branchante dans un environnement inhomogène en temps, au sens où la loi des accroissements varie en fonction du temps. On compare avec des modèles connus ou simplifiés, en particulier le modèle i.i.d., où l’on observe des marches aléatoires indépendantes et le modèle de la marche aléatoire homogène. On s’intéresse par la suite aux corrélations entre les particules maximales d’un mouvement brownien branchant. Plus précisément, on étudie le temps de branchement entre deux particules maximales. Finalement, on applique les méthodes et les résultats des premiers chapitres afin d’étudier les corrélations dans un mouvement brownien branchant dans un environnement inhomogène. Le résultat principal du mémoire stipule qu’il y a existence de temps de branchement au centre de l’intervalle [0, t] dans le mouvement brownien branchant inhomogène, ce qui n’est pas le cas pour le mouvement brownien branchant standard. On présentera également certaines simulations numériques afin de corroborer les résultats numériques et pour établir des hypothèses pour une recherche future.

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined

Exercise sheet 2 pdf

Exercises and solutions in PDF

Exercise sheet 1 pdf

Exercises and solutions in PDF

Exam 1988 pdf

Exam and solutions in PDF

Exercise sheet 1

Exercises and solutions in LaTex

Exercise sheet 2

Exercises and solutions in LaTex

Exam 1988

Exam and solutions in LaTex

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

La disonancia cognitiva y trampa de la memoria en decisiones de Inversión: caso colombiano

Este documento es el resultado de una investigación bajo el enfoque de Finanzas Corporativas del Comportamiento, disciplina relevante en el mundo financiero desde el 2002 y que hasta el momento poco se ha investigado en Colombia. Esta difiere del supuesto tradicional de la racionalidad de los individuos en la toma de decisiones financieras, ya que pueden ser influenciadas por sesgos cognitivos y emocionales que la teoría ortodoxa no tiene en cuenta en sus supuestos. Esta investigación busca indagar, desde el punto de vista conceptual y mediante el análisis de resultados de estudio de campo con operadores del mercado bursátil colombiano, sobre la posible presencia de elementos comportamentales en las decisiones de inversión. Los sesgos que se evaluaron fueron: disonancia cognitiva, heurístico de disponibilidad y sesgo de confirmación. Para la recolección de fuentes primarias, una encuesta fue enviada a los operadores Colombianos, categorizados en operadores con experiencia y operadores jóvenes. Después del filtro, 142 encuestas fueron seleccionadas para el análisis. Los principales hallazgos fueron que los jóvenes son más propensos a experimentar disonancia cognitiva y heurístico de disponibilidad y en ambas categorías, los sesgos analizados influencian medianamente la toma de decisiones de inversión.

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.