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Partial Differential Equation Approach for Valuation of European Put Option Price using Two Stochastic Financial Models.
No full textAn option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) at or before the expiration date of the option. This paper looked at two different models in finance which are the Constant Elasticity of Variance (CEV) model and the Black-Karasinski model. We obtained the various Partial Differential Equations (PDEs) option price valuation formulas for these two models using the riskless portfolio method through the elimination of the stochastic components from their respective Stochastic Differential Equations (SDEs). Also, numerical implementation of the derived Black-Scholes Parabolic PDEs options pricing equations for the SDEs models was carried out using the Explicit Finite Difference method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE) show the various effects of increase in the underlying asset value (stock price) and increase in the risk free interest rate on the value of the European Put Option for these models. From the results, we see that an increase in the stock price and interest rate both yields a decrease in the value of the option price and hence guides the holder of the option with quality decision to not exercise his right on the option and may allow the option to expir
MHD Micropolar Fluid Flow Over a Permeable Stretching Sheet in the presence of Variable Viscosity and Thermal Conductivity with Soret and Dufour Effects.
No full textThis study investigated the heat and mass transfer behaviour of thermally radiating and chemically reacting MHD Micropolar fluid over a permeable stretching sheet in a Darcy-Forchheimer porous medium under the influence of temperature dependent viscosity and thermal conductivity. The effects of Soret and Dufour in the presence of non-uniform heat source/sink are also examined. The coupled nonlinear partial differential equationsgoverning the fluid flow are transformed into coupled nonlinear ordinary differential equations by applying Lie-group scaling transformations. The resulting coupled nonlinear ODEs are solved by means of Weighted residuals method (WRM) and the obtained solution compared with shooting technique alongside fourth order Runge-Kutta method. The influences of the emerging flow parameters on the dimensionless velocity, microrotation, temperature and species concentration profiles are graphically presented while the effects of some selected flow parameters on the skin friction coefficient, wall couple stress, heat and mass transfer rates are tabulated
Coupled best proximity points of generalised Hardy-Rogers type cyclic (w)-contraction mappings
No full textIn this paper, we introduce generalized Hardy-Rogers type cyclic (w)- contraction mappings which generalizes the cyclic, Kannan, Chatterjeaand Reich contraction mappings. We establish the existence and uniqueness of coupled best proximity points of such mappings in the frameworkof b-metric space. Some examples are presented to support the results proved herein. Our results generalize and extend various comparable resultsin the existing literature. An application of our result to establish the existence of a solution of a differential equation is presented
The Beta-Modified Weighted Rayleigh Distribution: Application to Virulent Tubercle Disease
No full textFlexible parametric models are useful for modeling survival data and this has become an important field in statistics; and concern of statisticians in data analysis. Therefore, this paper presents a univariate model called Beta modified weighted Rayleigh distribution constructed from modified weighted Rayleigh distribution. The new distribution is achieved by introducing two shape parameters to the existing modified Weighted Rayleigh distribution using logit of beta function. The idea is to verify if the Beta modified Weighted Rayleigh distribution would perform better than modified Weighted Rayleigh distribution in modeling survival data. The statistical properties such as; survival rate, hazard rate, moment generating functions, skewness and kurtosis are determined for the new distribution. We also performed the expected estimation of model parameters by maximum likelihood. The Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Consistent Akaike Information Criterion (CAIC) are employed to select the best model. The superiority and flexibility of the proposed distribution is illustrated and applied to survival times of guinea pigs with virulent tubercle data sets. The results with the baseline distribution are also compared. Likewise, results from the modelselection criteria: the AIC, BIC and CAIC favoured BMWR; indicating that the proposed distribution performs and has better representation of the data than the MWR distribution. 
New Subclasses of Univalent Functions Defined Using a Linear Combination of Generalised S?al?agean and Ruscheweyh Operators
No full textStress-Work and Chemical Reaction Effects on MHD Forced Convection Heat and Mass Transfer Slip-Flow Towards A Convectively Heated Plate In A Non-Darcian Porous Medium With Surface Mass-Flux
No full textAnalysis is conducted numerically on forced-convective heat and reactive solute mass transfer of a steady incompressible, electrically conducting, chemically reacting and Joule dissipating viscous fluid streaming towards a stationary porous planar surface embedded in a saturated non-Darcian porous medium in the presence of surface mass flux, pressure stress-work and velocity slip. The governing coupled nonlinear boundary layer partial differential equations are transformed by existing similarity variables into a set of nonlinear, ordinary differential equations in conjunction with the accompanying boundary conditions and then solved using a shooting quadrature along with fourth order Runge-Kutta integration scheme. The features of the flow, heat and mass transfer characteristics as per the skin friction coefficient, heat and mass transfer rates subject to simulated values of the Darcian number, Forchheimer number, Prandtl number, Eckert number, Schmidt number, reaction rate and order, mass flux (transpiration) and Biot number are analysed and discussed by means of tables while the dimensionless temperature, velocity and concentration profiles are captured through graphs. All these basic flow parameters bear significant influences on the flow