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A note on (dis)investment options and perpetuities under CIR interest rates
Larguinho, Manuela; Dias, José Carlos; Braumann, Carlos A.In this chapter, we discuss alternative ways of computing the oprions to invest in and divest from an investment project in a CIR economy (Cox et al., Ecomometrica 53(2): 385-408, 1985). Moreover, different methods of determining CIR perpetuities will also be analysed.
On the computation of option prices and Greeks under the CEV model
Larguinho, Manuela; Dias, José Carlos; Braumann, Carlos A.Pricing options and evaluating Greeks under the constant elasticity of variance (CEV) model requires the computation of the non-central chi-square distribution function. In this article, we compare the performance, in terms of accuracy and computational time, of alternative methods for computing such probability distributions against an externally tested benchmark. In addition, we present closed-form solutions ...
Allee effects in randomly varying environments
Braumann, Carlos A.; Carlos, ClaraBased on a deterministic model of population growth with Allee effects, we propose a general stochastic model that incorporates environmental random fluctuations in the growth process. We study the model properties, existence and uniqueness of solution and the staionary behavior. We also obtain expressions for the first passage times, in particular, the mean and standard deviation of the extinction times for th...
Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and...
da Silva, João Lita; Caeiro, Frederico; Natário, Isabel; Braumann, Carlos A.; Esquível, Manuel L.; Mexia, João TiagoSelected papers of the 17th Congress of the Portuguese Statistical Society, covering recent advances in Statistics, particularly in Regression, Extreme values, Markov processes and statistical applications in several areas.
Absolute diffusion process: sensitivity measures
Larguinho, Manuela; Dias, José Carlos; Braumann, Carlos A.The constant elasticity of variance (CEV) model of Cox (Notes on Option Pricing I: Constant Elasticity of Variance Diffusions, Working paper, Stanford University (1975)) captures the implied volatility smile that is similar to volatility curves observed in practice. The diffusion process has been used for pricing several financial option contracts. In this paper we present the analytical expressions of sensitiv...
Multiphasic Individual Growth Models in Random Environments
Filipe, Patrícia A.; Braumann, Carlos A.; Roquete, Carlos J.The evolution of the growth of an individual in a random environment can be described through stochastic differential equations of the form dY(t) = β(α − Y(t))dt + σdW(t), where Y(t)= h(X t ), X(t) is the size of the individual at age t, h is a strictly increasing continuously differentiable function, α = h(A), where A is the average asymptotic size, and β represents the rate of approach to maturity. The parame...
Multiphasic individual growth models in random environments
Filipe, Patrícia A.; Braumann, Carlos A.; Roquete, Carlos J.The evolution of the growth of an individual in a random environment can be described through stochastic differential equations of the form dY(t) = b(a-Y(t))dt+sdW(t), where Y(t)=h(X(t)), X(t) is the size of the individual at age t, h is a strictly increasing continuously differentiable function, a=h(A), where A is the average asymptotic size, and b represents the rate of approach to maturity. The parameter s m...
Stochastic Differential Equations General Models of Individual Growth in Uncert...
Braumann, Carlos A.; Filipe, Patrícia A.; Carlos, Clara; Roquete, Carlos J.Individual animal growth in a randomly varying environment is modeled using stochastic differential equation models. These models are generalizations of the classical deterministic growth models used in regression methods, but incorporate a random dynamical term describing the effects of environmental and other random fluctuations on the growth process. We describe parameter estimation and prediction methods, i...
Modelling Animal Growth in Random Environments: An Application Using Nonparamet...
Filipe, Patrícia A.; Braumann, Carlos A.; Brites, Nuno M.; Roquete, Carlos J.We study a stochastic differential equation growth model to describe individual growth in random environments. In particular, in this paper, we discuss the estimation of the drift and the diffusion coefficients using nonparametric methods for the case of non-equidistant data for several trajectories. We illustrate the methodology by using bovine growth data. Our goal is to assess: a) if the parametric models (w...
Equações diferenciais estocásticas e aplicações biológicas
Braumann, Carlos A.Invited dissemination paper on biological applications of stochastic differential equations.
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