1,721,161 research outputs found
Applications of Lévy processes in credit and volatility modelling
Full text linkMarket participants are faced with the problem of finding a good trade-off between the model adequacy and its tractability. The aim of this thesis is to develop tractable and intuitive models in the credit and equity areas and to assess their performance according to different criteria of interest for practitioners. Although sometimes criticized for its inability to reproduce quoted option prices which manifests itself in what is commonly referred to as the volatility smile, the Black-Scholes model and its implied volatility are widespread and their success is due to their very simple and intuitive concept. The first contribution of this thesis consists of the introduction of two kinds of alternative implied volatility, namely the implied Lévy space volatility and the implied Lévy time volatility, and of the investigation of the resulting skew adjustment. Moreover, we show that under the Lévy parameter settings, the model performs systematically better than the classical Black-Scholes model as regards the risk of the commonly used delta hedging strategy. This is illustrated by looking at the daily hedging error and P&L distributions and by noting that, for the Lévy models under investigation, the empirical variance is smaller and, for a wide range of in the money options, the empirical acceptability indices are higher than in the Black-Scholes setting. The second part of this thesis illustrates the impact of calibration risk under the He-ston model. In particular, we show that different plausible calibration procedures lead to different optimal parameter sets and hence to significantly different prices for a wide range of exotic products, emphasizing the necessity to take into account some additional safety margin for the pricing of these structured products, as it has been recommended in a recent directive of the Basel committee. The third contribution consists of the extension of the aVG model where the constraints on the subordinator parameters are relaxed such that the calibration does not require the existence of a liquid multivariate derivatives market which is nowadays pretty rare since the marginal characteristic functions become dependent on the whole parameter set. Moreover, the stocks log-return volatility, which is an indicator of the trading volume, becomes dependent on both the idiosyncratic and common subordinator settings, making the generalized model more coherent with the empirical evidence of the presence of both an idiosyncratic and a common component in the business clock. Furthermore we emphasize the presence of model risk inside a particular class of multivariate models by pricing standard multivariate options. Finally, we compare the exponential Lévy model with the classical Gaussian copula model for the pricing of CDO-squared tranches, using several approximations of the recursive approach, namely a full Monte Carlo approximation and a Monte Carlo approximation which rests either on the multivariate Normal approximation of the joint inner CDO loss distribution or on the multivariate Poisson approximation of the joint number of defaults affecting the inner CDOs. The numerical study shows in particular that the multivariate Poisson approximation method outperforms the multivariate Normal approximation for CDOs-squared made up of inner equity tranches
The number of overlapping customers
Full text linkWe consider the number of overlapping customers in several single- and multiserver queues, i.e., the number of customers whose visit to a service system at some point in time has an overlap with that of a tagged customer. Restricting ourself to the FCFS policy, we obtain the probability generating function and moments of the number of overlaps in the M/G/1, M/G/1/N, M/M/c and G/M/c queue and (as an approximation) the M/G/c queue.</p
Applied probability meets Bessel, Hermite, Kummer, Tricomi, Wiener & Hopf (and also Ornstein & Uhlenbeck)
No full textWe discuss a few applied probability models: a blood bank model, an insurance risk model and a queueing/inventory model. In each case, the process under study {X(t), t ≥ 0} has state space (−∞, ∞).
In the blood bank case, X(t) indicates the amount of blood present at time t, if there is a positive amount present; otherwise, −X(t) denotes the total amount that is being demanded.
In the insurance risk case, X(t) indicates the capital at time t, if there is a positive amount present; otherwise, −X(t) denotes the shortage. It is agreed that ruin does not immediately occur when X(t) becomes negative, but the process ends (bankruptcy) according to a bankruptcy rate function ω(−X(t)) when X(t) < 0.
In the queueing/inventory model, X(t) indicates the amount of work present at time t, if there is a positive amount present; if no work is present, the tireless server keeps working, building up an inventory, and −X(t) then denotes the inventory level. The inventory is removed at a rate ω(−X(t)).
Under Poisson assumptions for the various arrival processes (of blood donations and blood requirements; of claims; of service requirements) and ergodicity conditions we try to determine the steady-state distributions of the X(t) processes; in the insurance risk model, we determine the bankruptcy probability. This appears to involve various special functions, like those of Bessel, Hermite, Kummer and Tricomi.Non UBCUnreviewedAuthor affiliation: Eindhoven University of TechnologyFacult
Polling - analysis, optimization and control
No full textInternational audienceA polling model is a queueing model consisting of several queues, which are cyclically visited by a server. The server visits the queues according to some discipline, like -limited (serve at most one customer in a visit) or exhaustive (serve a queue until it has become empty). Polling models find many applications in computer-communications, and also in other areas like maintenance, production-inventory systems, and signallized traffic intersections. The first part of the talk contains a global introduction to polling systems, and a review of some of their key properties. In the second part of the talk I'd like to describe some recent and ongoing work with Kamil Kosi\'nski and Offer Kella (on joint queue length and joint workload distributions) and with Ivo Adan, Urtzi Ayesta, Josine Bruin, Brian Fralix, Vidyadhar Kulkarni, Maaike Verloop, Adam Wierman and Erik Winands (on various scheduling and optimization problems in polling systems)
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Rush hour roulette and the public transport choice
No full textWe focus on rush hour congestion on a macroscopic scale. When there is limited traffic, travel times are hardly influenced by the presence of traffic. In contrast, when there is a lot of traffic, the presence of other users has a severe impact on travel times through the finite capacity of the road infrastructure. Therefore we propose to model congestion at a macroscopic scale by a Markovian level-dependent queueing system, service rates being sub-linear in terms of the queue content. We assess the choice between private and public transport in two cases. Assuming that the arrival rate is constant over time and that the cost of public transport is expressed in terms of waiting time, we determine the proportion of users taking public transport at the Wardrop equilibrium and compare with the socially optimal proportion. Moreover, for a particular choice of level-dependent rates we show equivalence of the queueing system at hand with a discriminatory processor sharing system with permanent customers. We then relax the assumption of having constant arrival rates. In particular, we study the fluid limit of the time-dependent (and level-dependent) system and again focus on the proportion of users that take public transport
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Overflow probabilities for Markov-modulated infinite-server queues: a large-deviations approach
No full textIn this paper we consider an infinite-server queue in a random environment. The distinguishing feature of the model is the presence of two irreducible Markov chains: one Markov chain modulates the arrival rates, while the other modulates the service times. We are interested in the probability that the number of jobs in the system becomes unusually large, i.e. we are interested in overflow.
Because arrival rates and service times are stochastically varying over time, the number of jobs in the system has a Poisson distribution with random parameters rather than a 'classical' Poisson distribution. In this case we cannot use a CLT-type result to analyze the system. However, basic large-deviations techniques provide an alternative approach. Scaling the arrival rates linearly, we prove a large-deviations principle by conditioning on paths of the background processes that are very likely to lead to overflow. We show that, conditional on these paths, we are in a situation in which Cramér's Theorem may be applied. This gives us the rate function for the number of jobs in the system and we use it to describe overflow probabilities. A nice observation is that we do not need to know the transition probabilities of the Markov chains to say something about overflow probabilities
- …
