Pricing executive stock options under employment shocks

We obtain explicit expressions for the subjective, objective and market value of perpetual executive stock options (ESOs) under exogenous employment shocks driven by an independent Poisson process. Within this setup,we obtain the executive's optimal exercise policy which allows us to analyze the determinants of both, the subjective valuation by executives and the objective valuation by firms. The perpetual ESO is compared with the more realistic finite maturity ESO finding that the approximation is reasonably good. We also use the objective valuation's results for accounting purposes. Further,we analyze the objective valuation distribution when there is uncertainty about the employment shock parameter. Finally, the role of ESOs in the design of executive's incentives is also discussed.ESO, Risk Aversion, Undiversification, Incentives, FAS 123R.

Statistics of the Optical Phase of a Gain-Switched Semiconductor Laser for Fast Quantum Randomness Generation

The statistics of the optical phase of the light emitted by a semiconductor laser diode when subject to periodic modulation of the applied bias current are theoretically analyzed. Numerical simulations of the stochastic rate equations describing the previous system are performed to describe the temporal dependence of the phase statistics. These simulations are performed by considering two cases corresponding to random and deterministic initial conditions. In contrast to the Gaussian character of the phase that has been assumed in previous works, we show that the phase is not distributed as a Gaussian during the initial stages of evolution. We characterize the time it takes the phase to become Gaussian by calculating the dynamical evolution of the kurtosis coefficient of the phase. We show that, under the typical gain-switching with square-wave modulation used for quantum random number generation, quantity is in the ns time scale; that corresponds to the time it takes the system to lose the memory of the distribution of the initial conditions. We compare the standard deviation of the phase obtained with random and deterministic initial conditions to show that their differences become more important as the modulation speed is increased.This research was funded by Ministerio de Economía y Competitividad (MINECO/FEDER,UE), Spain under grant RTI2018-094118-B-C22

Particle resolved model of gas-flow inside a pipe with pellet filling

Algunos métodos prometedores de almacenamiento de hidrógeno basan su funcionamiento en los reactores de lecho fijo. El CFD es una herramienta muy útil en el diseño de dichos reactores, ya que permite realizar precisas predicciones de comportamiento con un bajo coste. Estas aproximaciones del proceso son muy útiles para determinar el tamaño y forma óptimos del reactor, así como de las partículas de su interior. Sin embargo, el gran esfuerzo computacional que implican los modelos más detallados, hace que este método no sea siempre la opción preferida. El objetivo de este trabajo es describir el proceso de generación y validación de un modelo computacional PRCFD de un reactor de lecho fijo relleno de partículas esféricas, el estudio de la influencia de algunas de sus características y la comparación de los resultados de pérdida de presión con los de un modelo empírico usando la ecuación de Ergun.Departamento de Ingeniería de Sistemas y AutomáticaGrado en Ingeniería en Tecnologías Industriale

Incorporating boundary conditions in a stochastic volatility model for the numerical approximation of bond prices

Producción CientíficaIn this paper, we consider a two-factor interest rate model with stochastic volatil-ity, and we assume that the instantaneous interest rate follows a jump-diffusionprocess. In this kind of problems, a two-dimensional partial integro-differentialequation is derived for the values of zero-coupon bonds. To apply standardnumerical methods to this equation, it is customary to consider a boundeddomain and incorporate suitable boundary conditions. However, for thesetwo-dimensional interest rate models, there are not well-known boundary con-ditions, in general. Here, in order to approximate bond prices, we propose newboundary conditions, which maintain the discount function property of thezero-coupon bond price. Then, we illustrate the numerical approximation ofthe corresponding boundary value problem by means of an alternative directionimplicit method, which has been already applied for pricing options. We testthese boundary conditions with several interest rate pricing models.MEC-FEDER Grant MTM2017-85476-C2-P, Junta de Castilla y León Regional Grants VA041P17 (with European FEDERFunds), VA138G18 y VA148G1

Irregular pulsating polarization dynamics in gain-switched vertical-cavity surface-emitting lasers

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.International audienceIn this paper, we report on experimental and theoretical investigation on the nonlinear dynamics of the two orthogonal linearly polarized fundamental transverse modes of verticalcavity surface-emitting lasers (VCSELs) under sinusoidal current modulation. Irregular pulses of the power of individual polarizations are measured with a period equal to twice the modulation period. In contrast with individual polarizations, total power displays regular pulsing at twice the modulation period. The variability of pulse streams is characterized by using residence times distributions. We show that the residence time distributions for individual linear polarizations display an exponential decay for large values of that time. Those results are well reproduced by using a theoretical model that includes spontaneous emission fluctuations. However the previous qualitative features remain even in the absence of spontaneous emission noise. Our results therefore suggest that the irregular polarization dynamics have a deterministic origin and can be defined as deterministic chaos

Anomalous transport in second order hydrodynamics

We study the non-dissipative transport effects appearing at second order in the hydrodynamic expansion for a non-interacting gas of chiral fermions by using the partition function formalism. We discuss some features of the corresponding constitutive relations, derive the explicit expressions for the conductivities and compare with existing results in the literature

Thermodynamics of Resonant Scalars in AdS/CFT and implications for QCD

We explore the thermodynamics of a simple 5D Einstein-dilaton gravity model with a massive scalar field, with asymptotically AdS behavior in the UV. The holographic renormalization is addressed in details, and analytical results are obtained at high temperatures. We study the power corrections predicted by the model, and compare with lattice data in the deconfined phase of gluodynamics. Finally, it is discussed the role played by the conformal anomaly for integer values of the dimension of the condensate dual to the scalar field.This work has been supported by Plan Nacional de Altas Energias grant FPA2012-34456, Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042) and by the Basque Government under grant IT559-10. The research of E.M. is supported by the European Union under a Marie Curie Intra-European Fellowship (FP7-PEOPLE-2013-IEF) with project number PIEF-GA-2013-623006

Polynomial adjusted Student-t densities for modeling asset returns

We present a polynomial expansion of the standardized Student-t distribution. Our density, obtained through the polynomial adjusted method in Bagnato, Potí, and Zoia (2015. “The Role of Orthogonal Polynomials in Adjusting Hyperbolic Secant and Logistic Distributions to Analyse Financial Asset Returns.” Statistical Papers 56 (4): 1205–12340), is an extension of the Gram–Charlier density in Jondeau and Rockinger (2001. “Gram-Charlier Densities.” Journal of Economic Dynamics and Control 25 (10): 1457–1483). We derive the closed-form expressions of the moments, the distribution function and the skewness–kurtosis frontier for a well-defined density. An empirical application is also implemented for modeling heavy-tailed and skewed distributions for daily asset returns. Both in-sample and backtesting analysis show that this new density can be a good candidate for risk management.Financial support from the Spanish Ministry of Economy and Competitiveness through grant ECO2017-87069-P is gratefully acknowledged by Ángel León

Investment option under CIR interest rates

We analyze extensively the characteristics of the solution to an irreversible investment decision when the only source of uncertainty comes from interest rates. They are assumed to be driven by the popular Cox–Ingersoll–Ross (CIR) stochastic process. Particular attention is paid to the impact that both CIR parameters and risk aversion have on the threshold rate.Financial support from the Spanish Ministry of Education and Science through the grant SEJ 2005-09372 (Leon) and SEJ 2004-05815 (Carmona) is gratefully acknowledged

Pandemic effects in the Solow growth model

We show how diseases can affect economic growth in a Solow growth model, with population growth and no technical progress, but modified to include a saving rate that depends on the individual health status. We successively insert this model into the SIS (susceptible–infected–susceptible) and SIR (susceptible–infected–recovered) models of disease spreading. In these two models, the spread of the infection proceeds according to the so-called basic reproductive number. This number determines in which of the two possible equilibria, the disease-free or the pandemic equilibrium, the economy ends. We show that output per capita is always lower in the pandemic steady state, which implies a contraction in the economy's production possibilities frontier.Julio Carmona acknowledges the financial support from the Spanish Ministerio de Economía y Competitividad, through the project ECO2016-77200-P. Ángel León acknowledges the financial support from the Spanish Ministerio de Economía y Competitividad, through grant PID2021-124860NB-I00