Calibration of stochastic volatility models via second order approximation: the Heston model case

Using a suitable Hull and White type formula we develop a methodology to obtain asecond order approximation to the implied volatility for very short maturities. Using thisapproximation we accurately calibrate the full set of parameters of the Heston model. Oneof the reasons that makes our calibration for short maturities so accurate is that we alsotake into account the term-structure for large maturities. We may say that calibration isnot "memoryless", in the sense that the option's behavior far away from maturity doesinfluence calibration when the option gets close to expiration. Our results provide a wayto perform a quick calibration of a closed-form approximation to vanilla options that canthen be used to price exotic derivatives. The methodology is simple, accurate, fast, andit requires a minimal computational cost.

Avalanches in a fluctuationless first-order phase transition in a random-bond Ising model

We study the behavior of the random-bond Ising model at zero temperature by numerical simulations for a variable amount of disorder. The model is an example of systems exhibiting a fluctuationless first-order phase transition similar to some field-induced phase transitions in ferromagnetic systems and the martensitic phase transition appearing in a number of metallic alloys. We focus on the study of the hysteresis cycles appearing when the external field is swept from positive to negative values. By using a finite-size scaling hypothesis, we analyze the disorder-induced phase transition between the phase exhibiting a discontinuity in the hysteresis cycle and the phase with the continuous hysteresis cycle. Critical exponents characterizing the transition are obtained. We also analyze the size and duration distributions of the magnetization jumps (avalanches).

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.

A proposal for a new specification for a conditionally heteroskedastic variance model: the Quadratic Moving-Average Conditional Heteroskedasticity and an application to the D. Mark-U.S. dollar Exchange Rate

Ever since the appearance of the ARCH model [Engle(1982a)], an impressive array of variance specifications belonging to the same class of models has emerged [i.e. Bollerslev's (1986) GARCH; Nelson's (1990) EGARCH]. This recent domain has achieved very successful developments. Nevertheless, several empirical studies seem to show that the performance of such models is not always appropriate [Boulier(1992)]. In this paper we propose a new specification: the Quadratic Moving Average Conditional heteroskedasticity model. Its statistical properties, such as the kurtosis and the symmetry, as well as two estimators (Method of Moments and Maximum Likelihood) are studied. Two statistical tests are presented, the first one tests for homoskedasticity and the second one, discriminates between ARCH and QMACH specification. A Monte Carlo study is presented in order to illustrate some of the theoretical results. An empirical study is undertaken for the DM-US exchange rate.

Model-based diagnosis system: application to constructed wetlands

Report for the scientific sojourn carried out at the Model-based Systems and Qualitative Reasoning Group (Technical University of Munich), from September until December 2005. Constructed wetlands (CWs), or modified natural wetlands, are used all over the world as wastewater treatment systems for small communities because they can provide high treatment efficiency with low energy consumption and low construction, operation and maintenance costs. Their treatment process is very complex because it includes physical, chemical and biological mechanisms like microorganism oxidation, microorganism reduction, filtration, sedimentation and chemical precipitation. Besides, these processes can be influenced by different factors. In order to guarantee the performance of CWs, an operation and maintenance program must be defined for each Wastewater Treatment Plant (WWTP). The main objective of this project is to provide a computer support to the definition of the most appropriate operation and maintenance protocols to guarantee the correct performance of CWs. To reach them, the definition of models which represent the knowledge about CW has been proposed: components involved in the sanitation process, relation among these units and processes to remove pollutants. Horizontal Subsurface Flow CWs are chosen as a case study and the filtration process is selected as first modelling-process application. However, the goal is to represent the process knowledge in such a way that it can be reused for other types of WWTP.

A nonlinear threshold model for the dependence of extremes of stationary sequences

One of the main implications of the efficient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stocks prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example. JEL classification: C12; C15; C22; C51 Keywords and Phrases: asymmetries, crises, extreme values, hypothesis testing, leverage effect, nonlinearities, threshold models

A General model of bilateral migration agreements

Unilateral migration policies impose externalities on other countries. In order to try to internalize these externalities, countries sign bilateral migration agreements. One element of these agreements is the emphasis on enforcing migration policies: immigrant-receiving countries agree to allow more immigrants from their emigrant-sending partner if they cooperate in enforcing their migration policy at the border. I present a simple theoretical model that justifies this behavior in a two-country setting with welfare maximizing governments. These governments establish migration quotas that need to be enforced at a cost. I prove that uncoordinated migration policies are inefficient. Both countries can improve welfare by exchanging a more "generous" migration quota for expenditure on enforcement policy. Contrary to what could be expected, this result does not depend on the enforcement technology that both countries employ.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.

La integració de les energies renovables en un model energètic sostenible

La sostenibilitat del model energètic de Catalunya es veu condicionada per aspectes com la dependència energètica, la seguretat de subministrament, l’eficiència energètica, els impactes ambientals i la demanda creixent. D’altra banda, la incorporació d’energia renovable en el mix energètic implica una major autonomia energètica, seguretat de subministrament a llarg termini, i eficiència energètica, així com un menor impacte ambiental. Tanmateix, la contribució en el sistema elèctric d’un volum ja important i creixent d’energia renovable requereix una complexa tasca d’integració a nivell tècnic i econòmic. Per aconseguir-ho, és necessari desenvolupar una regulació estable que complementi el procés de liberalització del sector amb l’objectiu d’acomodar la generació renovable en un model energètic sostenible. La (in)formació i participació de la demanda es presenta com una condició clau per engegar el camí cap a una nova cultura energètica.

Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

Creació i transmissió de coneixement als clústers empresarials: un model de simulació

Projecte de recerca elaborat a partir d’una estada a l’Snider Entrepreneurial Research Center de la Wharton School de la University of Pennsilvanya y, EUA entre juliol i desembre del 2007. L’objectiu d’aquest projecte és estudiar la relació entre les estratègies de gestió del coneixement i les tecnologies de la informació i la comunicació (TIC) en l’evolució de les poblacions d’organitzacions i els seus efectes en els patrons industrials d’aglomeració espacial. Per a això s’adopta una aproximació fonamentada en la utilització d'un model basats en agents per a obtenir hipòtesis significatives i provables sobre l’evolució de les poblacions d’organitzacions al si de clústers geogràfics. El model de simulació incorpora les perspectives i supòsits d’un marc conceptual, l’Espai de la Informació o I-Space. Això permet una conceptualització basada en la informació de l’entorn econòmic que té en compte les seves dimensions espacials i temporals. Mitjançant els paràmetres del model es dóna la possibilitat d’assignar estratègies específiques de gestió del coneixement als diversos agents i de localitzar-los en una posició de l’espai físic. La simulació mostra com l'adopció d'estratègies diverses pel que fa a la gestió del coneixement influeix en l'evolució de les organitzacions i de la seva localització espacial, i que aquesta evolució es veu modificada pel desenvolupament de les TIC. A través de la modelització de dos casos ben coneguts de clústers geogràfics d’alta tecnologia, com són Silicon Valley a Califòrnia i la Route 128 als voltants de Boston, s’estudia la interrelació entre les estratègies de gestió del coneixement adoptades per les empreses i la seva tria de localització espacial, i també com això és afectat per l’evolució de les tecnologies de la informació i de la comunicació (TIC). Els resultats obtinguts generen una sèrie d’hipòtesis de rica potencialitat sobre l’impacte del desenvolupament de les TIC en la dinàmica d’aquests clusters geogràfics. Concretament, es troba que la estructuració del coneixement i l’aglomeració espacial co-evolucionen i que aquesta coevolució es veu significativament alterada pel desenvolupament de les TIC.

Universitat i discapacitat: construint un model d’aula inclusiva en el marc universitari

La present investigació es centre en crear un programa de formació i assessorament docent per atendre la diversitat d’estudiants en el marc universitari mitjançant els principis del disseny universal de la instrucció (DUI). D’aquesta manera es pretén donar resposta: a) a la necessitat d’implementar un model pedagògic en el marc universitari que doni resposta a la diversitat d’estudiants, b) de formar i canviar actituds docents vers la discapacitat i c) d’adaptar el nou marc legislatiu espanyol en matèria de discapacitat a les aules de les nostres universitats. A través d’un procés d’investigació-acció es detecten quins són les necessitats i dificulats pedagògiques, dels docents de les diferents universitats catalanes, per construir espais educatius que garanteixin la igultat d’oportunitats als estudiants amb discapacitat. Les dades obtingudes ens permeten crear una proposta de formació pels docents universitaris, basada en el paradigma educatiu del disseny universal de la instrucció.

Influence of the in vivo deregulation of the expression of ntrk3 (trkc) on cortical development of a murine model of panic/anxiety disorder

Alteracions durant el desenvolupament cerebral produirien canvis en la connectivitat neuronal i la bioquímica cel•lular que podrien resultar en una disfunció cognitiva i/o emocional, desembocant a trastorns psiquiàtrics. Les neurotrofines intervenen en els processos del neurodesenvolupament i en la funcionalitat del cervell adult i, conseqüentment, serien bons candidats com a factors de predisposició en diverses malalties mentals. S’ha suggerit la implicació del receptor de la neurotrofina 3, TrkC, en el trastorn de pànic. Nosaltres proposem que la sobreexpressió del gen NTRK3 (TrkC) és un mediador comú dels desencadenants genètics i ambientals d’aquest trastorn. Concretament, la seva desregulació podria produir canvis estructurals i funcionals a l’escorça cerebral dels pacients pel seu paper durant l’establiment dels circuïts corticals i la neuroplasticitat a l’adult, probablement esdevenint elements de predisposició a patir atacs de pànic. Els objectius principals d’aquest treball han estat: 1/determinar la contribució específica del gen NTRK3 a les alteracions de l’escorça cerebral observades en pacients, utilitzant un model murí modificat genèticament (TgNTRK3), i 2/analitzar l’impacte específic de la sobreexpressió de NTRK3 sobre la corticogènesi durant estadis embrionaris o postnatals estudiant la neurogènesi i la neuritogènesi. Els resultats indiquen que la sobreexpressió de NTRK3 als ratolins produeix una reducció del gruix de l’escorça frontal, recapitulant la hipofrontalitat dels pacients, que comportaria una menor inhibició dels nuclis subcorticals del sistema límbic com l’amígdala, i alteracions citoarquitectòniques a l’escorça prefrontal medial que recolzen la hipòtesi del seu mal funcionament. Tanmateix, els ratolins TgNTRK3 presenten canvis estructurals a l’escorça somatosensorial, suggerint que el processament de la informació sensorial podria estar alterat, el que encara no s’ha explorat en pacients. La sobreexpressió de NTRK3 també afecta la neuritogènesi en cultius primaris corticals i modifica la resposta de les neurones a l’estimulació amb neurotrofines. Per tant, el fenotip cortical adult dels TgNTRK3 podria dependre d’alteracions durant la corticogènesi.

Chaos and order in the contemporary city. The impact of urban spatial structure on population density and commuting distance in Barcelona, 1986-2001.

One of the criticisms leveled at the model of dispersed city found all over the world is its unarticulated, random, and undifferentiated nature. To check this idea in the Barcelona Metropolitan Region, we estimated the impact of the urban spatial structure (CBD, subcenters and transportation infrastructures) over the population density and commuting distance. The results are unfavorable to the hypothesis of the increasing destructuring of cities given that the explanatory capacity of both functions improves over time, both when other control variables are not included and when they are included.