Thursday, October 20th 2022


Short Course
Cláudia Nunes Philippart and Conceição Amado (IST and
CEMAT)
Abstract:
The pricing of options is a standard problem in
finance. The Black Scholes model provides a
mathematical formulation to the pricing of these
products. In the first part of the course we present
the basics of mathematical finance that are useful
to explain the BlackScholes formula. We will also
discuss the assumptions behind the model. One of the
assumptions is constant volatility, which does not
hold in practice. So in the second part of the
course we discuss the volatility associated with
stock prices and we explain the concept of implied
volatility. We analyse some data concerning stock
prices and derive the implied volatility. In
particular we check for the stability of the
volatility during the pandemic crisis.

11:0012:30


Pricing of Options: from theory to
practice  Part I

14:3016:00


Pricing of Options: from theory to
practice  Part II

16:3018:00


Pricing of Options: from theory to
practice  Part III

Friday, October 21st 2022
10:0010:45


Helena Ribeiro (ESTG, Politécnico de
Leiria, and CEMAT)
Abstract:
Customer behavior upon arrival at a system plays a
very important role in analyzing the performance
and success of a service provider organization. In
current busy days, organizations increasingly deal
with impatient customers who often give up on
ordering the service due the number of customers
waiting in queue before them. The success of
organizations depends on minimizing such customer
losses, known in the queueing systems literature
as customer balking, while maintaining a
reasonable number of services per period of
continuous occupancy of their server. Aiming to
guide organizations in decision making to minimize
the balking problem, in this work we analyze
M^X/M/1/n systems with balking. These are queueing
systems with finite capacity, n, in which
customers arrive in batches according to a Poisson
process and are served by a single server, in a
first come first served discipline. The batch
sizes are independent and identically distributed.
The customer service times are independent and
identically exponential distributed random
variables and are independent of the arrival
process. Specifically, relying on the Markovian
structure of that systems, we derive the joint
probability function of the number of customers
served and the number of customers lost in periods
of continuous system occupancy (busyperiods), as
well as the respective marginal probability
functions. This is accomplished by proposing
efficient recursive procedures for the evaluation
of the corresponding probabilitygenerating
functions. The sensitivity analysis of such
systems measures is then performed.
Keywords: Queueing system; Batch arrival;
Balking; Busyperiod; Markov chain.

11:1512:00


Vanda Inacio (University of
Edinburgh)
Abstract:
The receiver operating characteristic (ROC)
surface is a popular tool for evaluating the
discriminatory ability of diagnostic tests
measured on a continuous scale when there exist
three ordered disease groups. Motivated by the
impact that covariates may have on the diagnostic
accuracy, and to safeguard against model
misspecification, we develop a flexible model for
conducting inference about the covariatespecific
ROC surface and its functionals. Specifically, we
postulate a locationscale regression model for
the test outcomes in each of the three disease
groups where the mean and variance functions are
estimated through penalisedsplines, while the
distribution of the error term is estimated via a
smoothed version of the empirical cumulative
distribution function of the standardised
residuals. Our simulation study shows that our
approach successfully recovers the true
covariatespecific volume under the surface and
optimal pair of thresholds in a variety of
scenarios. Our methods are motivated by and
applied to data derived from an Alzheimer's
disease study and we seek to assess the accuracy
of several potential biomarkers to distinguish
between individuals with normal cognition, mild
cognitive impairment, and dementia and how this
discriminatory ability may change with the age and
gender

12:0012:45


Idemauro de Lara (Universidade de São
Paulo)
Abstract:
Transition models are useful for analyzing
categorical longitudinal data, particularly when
the primary interest is in prediction. Thus, in
this work the basic ideas of this model class and
tests for stationarity are presented.
Additionally, it is noted that the methods
available for this model are directed to cases in
which the responses are individual. However, in
many areas, it is common to obtain grouped
categorical responses, that is, there are
different categories of response with the
registration of the number of individuals in each
one of them. As a motivation for the
methodological extension, a study applied to
agricultural sciences, involving Diaphorina citri,
which is a pest and vector of bacteria that
attacks citrus, is considered.
Keywords: stochastic process, transition
probabilities, maximum likelihood, entomology.

14:3015:15


Sandra Palau (Nacional Autonomous
University of Mexico, UNAM)
Abstract: Consider a critical Galton Watson tree
in varying environment. If the system survives
until a large time N, then choose k particles
uniformly from those alive. Consider the ancestral
tree drawn out by these particles. We are going to
discuss the shape of this ancestral tree. This is
a joint work with Simon Harris (Auckland, NZ) and
Juan Carlos Pardo (CIMAT, Mexico).

15:1516:00


Paula Milheiro (Faculty of
Engineering of the University of Porto and Center
for Mathematics of the University of Porto)
Abstract: The Design of Experiments (DoE) is a
statistical tool particularly relevant in the
study of new materials and new manufacturing
processes. It allows us to save time and money and
enables us analyse different options for combining
constituents of the material under study,
obtaining models and material optimisation. In
this talk we briefly introduce different currently
used DoE schemes and we focus on their use in some
practical situations: (a) improvement of building
materials manufacturing, including the
introduction of new constituents and new
manufacturing processes; (b) stabilization of
soils. The models that explain the material
response are conventional regression and Poisson
regression models. Emphasis will be given to
applications to real world problems.
Keywords: design of experiments, new materials
engineering, regression.

16:0016:45


João Paulo Martins (Escola Superior
de Saúde, P.Porto, CEAUL, Faculdade de Ciências,
Universidade de Lisboa)
Abstract: A systematic review is a research for
(primary) studies on some topic of interest whose
results are summarized. Metaanalysis is more than
a systematic review. It consists in a statistical
analysis of the summary findings of these primary
studies. This branch of Statistics has become
popular since the publication of some books about
this subject in the 80s of the last century. In
this talk, the fundamentals of any metaanalysis
are covered, i.e., how to measure an effect size,
as well as methods of combining the effect sizes
reported by the different primary studies.
Assumptions regarding the use of a fixed or random
effects model are also discussed. The different
steps that comprehend a metaanalysis are
analysed: the definition of the research question,
where and how to search for the studies, the
selection criteria, the assessment of the quality
and heterogeneity of the studies and the
publication bias, the presentation of the results
and the computation of a pooled estimate of the
effect size. The use of subgroup analysis and
metaregression to explain the heterogeneity of
the studies is also explored.
Keywords: Metaanalysis, systematic review,
pooled estimate, subgroup analysis,
metaregression.

