Search results for: Clarinda Vitorino Nhangumbe

Authors: Clarinda Vitorino Nhangumbe, Fredericks Ebrahim, Betuel Canhanga

Abstract:

The price of an option weather derivatives can be approximated as a solution of the two-dimensional convection-diffusion dominant partial differential equation derived from the Ornstein-Uhlenbeck process, where one variable represents the weather dynamics and the other variable represent the underlying weather index. With appropriate financial boundary conditions, the solution of the pricing equation is approximated using a nonstandard finite difference method. It is shown that the proposed numerical scheme preserves positivity as well as stability and consistency. In order to illustrate the accuracy of the method, the numerical results are compared with other methods. The model is tested for real weather data.

Keywords: nonstandard finite differences, Ornstein-Uhlenbeck process, partial differential equations approach, weather derivatives

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

Abstract:

Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: Clarinda V. Nhangumbe, Ercília Sousa

Abstract:

Weather Derivatives are financial instruments used to cover non-catastrophic weather events and can be expressed in the form of standard or plain vanilla products, structured or exotics products. The underlying asset, in this case, is the weather index, such as temperature, rainfall, humidity, wind, and snowfall. The complexity of the Weather Derivatives structure shows the weakness of the Black Scholes framework. Therefore, under the risk-neutral probability measure, the option price of a weather contract can be given as a unique solution of a two-dimensional partial differential equation (parabolic in one direction and hyperbolic in other directions), with an initial condition and subjected to adequate boundary conditions. To calculate the price of the option, one can use numerical methods such as the Monte Carlo simulations and implicit finite difference schemes conjugated with Semi-Lagrangian methods. This paper is proposed two explicit methods, namely, first-order upwind in the hyperbolic direction combined with Lax-Wendroff in the parabolic direction and first-order upwind in the hyperbolic direction combined with second-order upwind in the parabolic direction. One of the advantages of these methods is the fact that they take into consideration the boundary conditions obtained from the financial interpretation and deal efficiently with the different choices of the convection coefficients.

Keywords: incomplete markets, numerical methods, partial differential equations, stochastic process, weather derivatives

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Authors: Priscila Vitorino, Jeeziane Rezende, Edison Pereira, Adrielly Silva, Weimar Barroso

Abstract:

Body composition insight during physical activity is relevant to follow up sports income since it can be important and actuate in velocity, resistance, potency, and has an effect on force and agility. The purpose of this study was to identify anthropometric profile, evaluate and correlate body mass index and bioimpedance behavior during the days of Caminhada Ecológica de Goiás - Brasil. A longitudinal study was performed with 25 male participants, with an average age of 45.6±9.1 years. All patients were actives. Body composition was evaluated by body mass index (BMI) measurement and bioimpedance procedures. Both were collected 20 days before walking beginning (A0) and in the four days along the same (A1, A2, A3 e A4). Data were collected in the end of each walking day at athletes accommodations. Final distance during walking route was 308 km in five days, with an average of 62km/day and 7,6 km/hour, and an average temperature of 30°C. Data are represented with mean and standard deviation. ANOVA (Bonferroni pos test) was used to compare frequent measurements between the days. Pearson's correlation test was used to correlate BMI with lean mass, fat mass, and water. BMI decreased from A0 to A1, A2 and A3 (p < 0,01) and increased on A4 (p < 0,01). No changes were observed concerning fat percentage (p=0,60), lean mass (p=0,10) and body water composition (p=0,09). A positive and moderate correlation between BMI and fat percentage was observed; an inverse and moderate correlation between BMI, lean mass and body water composition occurred. Total body mass increased during high intensity and long term walking distance. However, the values of body fat, lean mass and water were maintained.

Keywords: aerobic exercise, body composition, metabolism, sports

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