Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

The transcription factor c-Maf controls touch receptor development and function.

The sense of touch relies on detection of mechanical stimuli by specialized mechanosensory neurons. The scarcity of molecular data has made it difficult to analyze development of mechanoreceptors and to define the basis of their diversity and function. We show that the transcription factor c-Maf/c-MAF is crucial for mechanosensory function in mice and humans. The development and function of several rapidly adapting mechanoreceptor types are disrupted in c-Maf mutant mice. In particular, Pacinian corpuscles, a type of mechanoreceptor specialized to detect high-frequency vibrations, are severely atrophied. In line with this, sensitivity to high-frequency vibration is reduced in humans carrying a dominant mutation in the c-MAF gene. Thus, our work identifies a key transcription factor specifying development and function of mechanoreceptors and their end organs.

Food for thought: the importance of glucose and other energy substrates for sustaining brain function under varying levels of activity.

The brain requires a constant and substantial energy supply to maintain its main functions. For decades, it was assumed that glucose was the major if not the only significant source of energy for neurons. This view was supported by the expression of specific facilitative glucose transporters on cerebral blood vessels, as well as neurons. Despite the fact that glucose remains a key energetic substrate for the brain, growing evidence suggests a different scenario. Thus astrocytes, a major type of glial cells that express their own glucose transporter, play a critical role in coupling synaptic activity with glucose utilization. It was shown that glutamatergic activity triggers an enhancement of aerobic glycolysis in this cell type. As a result, lactate is provided to neurons as an additional energy substrate. Indeed, lactate has proven to be a preferential energy substrate for neurons under various conditions. A family of proton-linked carriers known as monocarboxylate transporters has been described and specific members have been found to be expressed by endothelial cells, astrocytes and neurons. Moreover, these transporters are subject to fine regulation of their expression levels and localization, notably in neurons, which suggests that lactate supply could be adjusted as a function of their level of activity. Considering the importance of energetics in the aetiology of several neurodegenerative diseases, a better understanding of its cellular and molecular underpinnings might have important implications for the future development of neuroprotective strategies.

PPAR alpha structure-function relationships derived from species-specific differences in responsiveness to hypolipidemic agents.

The nuclear receptor PPAR alpha is a key regulatory transcription factor in lipid homeostasis, some liver detoxification processes and the control of inflammation. Recent findings suggest that many hypolipidemic drugs and anti-inflammatory agents can potentially act by binding to PPAR alpha and inducing its activity. Here, we identify some structure-function relationships in PPAR alpha, by using the species-specific responsiveness to the two hypolipidemic agents, Wy 14,643 and 5,8,11,14-eicosatetraynoic acid (ETYA). We first show that the species-specific differences are mediated primarily via the ligand binding domain of the receptor and that these two drugs are indeed ligands of PPAR alpha. By mutagenesis analyses we identify amino acid residues in the ligand binding domains of Xenopus, mouse and human PPAR alpha, that confer preferential responsiveness to ETYA and Wy 14,643. These findings will aid in the development of new synthetic PPAR alpha ligands as effective therapeutics for lipid-related diseases and inflammatory disorders.

Analytic behavior of the QED polarizability function at finite temperature

We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.

Modelos de tasas de interes en Chile: una revisión

Con este trabajo revisamos los Modelos de niveles de las tasas de intereses en Chile. Además de los Modelos de Nivel tradicionales por Chan, Karoly, Longstaff y Lijadoras (1992) en EE. UU, y Parisi (1998) en Chile, por el método de Probabilidad Maximun permitimos que la volatilidad condicional también incluya los procesos inesperados de la información (el modelo GARCH ) y también que la volatilidad sea la función del nivel de la tasa de intereses (modelo TVP-NIVELE) como en Brenner, Harjes y la Crona (1996). Para esto usamos producciones de mercado de bonos de reconocimiento, en cambio las producciones mensuales medias de subasta PDBC, y la ampliación del tamaño y la frecuencia de la muestra a 4 producciones semanales con términos(condiciones) diferentes a la madurez: 1 año, 5 años, 10 años y 15 años. Los resultados principales del estudio pueden ser resumidos en esto: la volatilidad de los cambios inesperados de las tarifas depende positivamente del nivel de las tarifas, sobre todo en el modelo de TVP-NIVEL. Obtenemos pruebas de reversión tacañas, tal que los incrementos en las tasas de intereses no eran independientes, contrariamente a lo obtenido por Brenner. en EE. UU. Los modelos de NIVELES no son capaces de ajustar apropiadamente la volatilidad en comparación con un modelo GARCH (1,1), y finalmente, el modelo de TVP-NIVEL no vence los resultados del modelo GARCH (1,1)

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Silencing of c-Fos expression by microRNA-155 is critical for dendritic cell maturation and function.

MicroRNAs (miRNAs) are small, noncoding RNAs that regulate target mRNAs by binding to their 3' untranslated regions. There is growing evidence that microRNA-155 (miR155) modulates gene expression in various cell types of the immune system and is a prominent player in the regulation of innate and adaptive immune responses. To define the role of miR155 in dendritic cells (DCs) we performed a detailed analysis of its expression and function in human and mouse DCs. A strong increase in miR155 expression was found to be a general and evolutionarily conserved feature associated with the activation of DCs by diverse maturation stimuli in all DC subtypes tested. Analysis of miR155-deficient DCs demonstrated that miR155 induction is required for efficient DC maturation and is critical for the ability of DCs to promote antigen-specific T-cell activation. Expression-profiling studies performed with miR155(-/-) DCs and DCs overexpressing miR155, combined with functional assays, revealed that the mRNA encoding the transcription factor c-Fos is a direct target of miR155. Finally, all of the phenotypic and functional defects exhibited by miR155(-/-) DCs could be reproduced by deregulated c-Fos expression. These results indicate that silencing of c-Fos expression by miR155 is a conserved process that is required for DC maturation and function.

Alterations of Neuromuscular Function after the World's Most Challenging Mountain Ultra-Marathon

We investigated the physiological consequences of the most challenging mountain ultra-marathon (MUM) in the world: a 330-km trail run with 24000 m of positive and negative elevation change. Neuromuscular fatigue (NMF) was assessed before (Pre-), during (Mid-) and after (Post-) the MUM in experienced ultra-marathon runners (n = 15; finish time = 122.43 hours +/-17.21 hours) and in Pre- and Post- in a control group with a similar level of sleep deprivation (n = 8). Blood markers of muscle inflammation and damage were analyzed at Pre- and Post-. Mean +/- SD maximal voluntary contraction force declined significantly at Mid- (-13+/-17% and -10+/-16%, P<0.05 for knee extensor, KE, and plantar flexor muscles, PF, respectively), and further decreased at Post- (-24+/-13% and -26+/-19%, P<0.01) with alteration of the central activation ratio (-24+/-24% and -28+/-34% between Pre- and Post-, P<0.05) in runners whereas these parameters did not change in the control group. Peripheral NMF markers such as 100 Hz doublet (KE: -18+/-18% and PF: -20+/-15%, P<0.01) and peak twitch (KE: -33+/-12%, P<0.001 and PF: -19+/-14%, P<0.01) were also altered in runners but not in controls. Post-MUM blood concentrations of creatine kinase (3719+/-3045 Ul.1), lactate dehydrogenase (1145+/-511 UI.L-1), C-Reactive Protein (13.1+/-7.5 mg.L-1) and myoglobin (449.3+/-338.2 microg.L-1) were higher (P<0.001) than at Pre- in runners but not in controls. Our findings revealed less neuromuscular fatigue, muscle damage and inflammation than in shorter MUMs. In conclusion, paradoxically, such extreme exercise seems to induce a relative muscle preservation process due likely to a protective anticipatory pacing strategy during the first half of MUM and sleep deprivation in the second half.

Cholesterol transport from late endosomes to the Golgi regulates t-SNARE trafficking, assembly, and function

Cholesterol regulates plasma membrane (PM) association and functioning of syntaxin-4 and soluble N-ethylmaleimide-sensitive fusion protein 23 (SNAP23) in the secretory pathway. However, the molecular mechanism and cellular cholesterol pools that determine the localization and assembly of these target membrane SNAP receptors (t-SNAREs) are largely unknown. We recently demonstrated that high levels of annexin A6 (AnxA6) induce accumulation of cholesterol in late endosomes, thereby reducing cholesterol in the Golgi and PM. This leads to an impaired supply of cholesterol needed for cytosolic phospholipase A2 (cPLA2) to drive Golgi vesiculation and caveolin transport to the cell surface. Using AnxA6-overexpressing cells as a model for cellular cholesterol imbalance, we identify impaired cholesterol egress from late endosomes and diminution of Golgi cholesterol as correlating with the sequestration of SNAP23/syntaxin-4 in Golgi membranes. Pharmacological accumulation of late endosomal cholesterol and cPLA2 inhibition induces a similar phenotype in control cells with low AnxA6 levels. Ectopic expression of Niemann-Pick C1 (NPC1) or exogenous cholesterol restores the location of SNAP23 and syntaxin-4 within the PM. Importantly, AnxA6-mediated mislocalization of these t-SNAREs correlates with reduced secretion of cargo via the SNAP23/syntaxin-4¿dependent constitutive exocytic pathway. We thus conclude that inhibition of late endosomal export and Golgi cholesterol depletion modulate t-SNARE localization and functioning along the exocytic pathway.

Dynamic modulation of CCR7 expression and function on naive T lymphocytes in vivo.

The chemokine receptor CCR7 is critical for the recirculation of naive T cells. It is required for T cell entry into secondary lymphoid organs (SLO) and for T cell motility and retention within these organs. How CCR7 activity is regulated during these processes in vivo is poorly understood. Here we show strong modulation of CCR7 surface expression and occupancy by the two CCR7 ligands, both in vitro and in vivo. In contrast to blood, T cells in SLO had most surface CCR7 occupied with CCL19, presumably leading to continuous signaling and cell motility. Both ligands triggered CCR7 internalization in vivo as shown in Ccl19(-/-) and plt/plt mice. Importantly, CCR7 occupancy and down-regulation led to strongly impaired chemotactic responses, an effect reversible by CCR7 resensitization. Therefore, during their recirculation, T cells cycle between states of free CCR7 with high ligand sensitivity in blood and occupied CCR7 associated with continual signaling and reduced ligand sensitivity within SLO. We propose that these two states of CCR7 are important to allow the various functions CCR7 plays in T cell recirculation.