Manuel Leote Esquivel

Prof. Dr. Manuel Leote Esquivel

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Academic Career Length

23Years (2004-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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27 March 2014 in Quantitative Finance
Verified
Journal Article
Closed access
PMPedro Mota
Pedro Mota
MEManuel Leote Esquivel
Manuel Leote Esquivel
1 February 2012 in Communications in Statistics - Simulation and Computation
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Journal Article
Open access
JSJ. Beleza Sousa
J. Beleza Sousa
MEManuel Leote Esquivel
Manuel Leote Esquivel
Raquel GasparRaquel Gaspar
Raquel Gaspar
In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.
8 February 2021 in Risks
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MEManuel Leote Esquivel
Manuel Leote Esquivel
Gracinda GuerreiroGracinda Guerreiro
Gracinda Guerreiro
MOMatilde C. Oliveira
Matilde C. Oliveira
PRPedroAlexandredaRosaCorteReal Corte Real
PedroAlexandredaRosaCorteReal Corte Real
We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light, moderate and severe dependence levels and the death state. For a general approach, we allow for non null intensities for all the returns from higher dependence levels to all lesser dependencies in the multi-state model. Using data from the 2015 Portuguese National Network of Continuous Care database, as the main research contribution of this paper, we propose a method to calibrate transition intensities with the one step transition probabilities estimated from data. This allows us to use non-homogeneous continuous time Markov chains for modeling Long-Term Care. We solve numerically the Kolmogorov forward differential equations in order to obtain continuous time transition probabilities. We assess the quality of the calibration using the Portuguese life expectancies. Based on reasonable monthly costs for each dependence state we compute, by Monte Carlo simulation, trajectories of the Markov chain process and derive relevant information for model validation and premium calculation.
30 June 2016 in Journal of Statistical Theory and Practice
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MEManuel Leote Esquivel
Manuel Leote Esquivel
PMPedro Mota
Pedro Mota
JMJoão Tiago Mexia
João Tiago Mexia
We extend some classical statistical inference to the case of a random number of observations with a stabilized distribution: namely, in the normal model, inference for the mean with known and unknown variance and inference for the variance. We describe some useful models for the number of observations obtained by truncation or translation of usual models given by integer-valued random variables: Poisson, binomial, geometric, and negative binomial. We present an efficient random search algorithm for the computation of the quantiles of the relevant statistics, we describe an interval estimation procedure for the extended model, and we propose a parametric bootstrap simulation study to validate the proposed procedure.
24 February 2024 in Mathematics
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MEManuel Leote Esquivel
Manuel Leote Esquivel
NKNadezhda Krasii
Nadezhda Krasii
Gracinda GuerreiroGracinda Guerreiro
Gracinda Guerreiro
We propose a method for fitting transition intensities to a sufficiently large set of trajectories of a continuous-time non-homogeneous Markov chain with a finite state space. Starting with simulated data computed with Gompertz–Makeham transition intensities, we apply the proposed method to fit piecewise linear intensities and then compare the transition probabilities corresponding to both the Gompertz–Makeham transition intensities and the fitted piecewise linear intensities; the main comparison result is that the order of magnitude of the average fitting error per unit time—chosen as a year—is always less than 1%, thus validating the methodology proposed.
3 July 2014 in Stochastic Models
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MEManuel Leote Esquivel
Manuel Leote Esquivel
JFJosé M. Fernandes
José M. Fernandes
Gracinda GuerreiroGracinda Guerreiro
Gracinda Guerreiro
In this paper, we study, by means of randomized sampling, the long-run stability of some open Markov population fed with time-dependent Poisson inputs. We show that state probabilities within transient states converge—even when the overall expected population dimension increases without bound—under general conditions on the transition matrix and input intensities. Following the convergence results, we obtain ML estimators for a particular sequence of input intensities, where the sequence of new arrivals is modeled by a sigmoidal function. These estimators allow for the forecast, by confidence intervals, of the evolution of the relative population structure in the transient states. Applying these results to the study of a consumption credit portfolio, we estimate the implicit default rate.