| 1 |
Author(s):
Amadi I. U., Nwaigwe E., Azor P. A..
Page No : 1-11
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Mathematical Analysis of Black-Scholes Partial Differential Equation on Stock Prices
Abstract
This paper is centered on Black-Scholes (BS) partial differential equation (PDE) and Crank-Nicolson (CN) numerical solutions for the valuation of European call option. In particular, Crank-Nicolson’s method was successfully applied to the transformed boundary value problems of European call option with results obtained. It was observed that Black-Scholes and Crank-Nicolson are impossible to differentiate but in terms of precisions Black-Scholes analytical values were found to be adequate. Also, a statistical test was performed, using Kolmogorov-Smirnov (KS) for goodness of fit test; results showed that BS and CN came from a common distribution. However, this paper presented here has a vital role in this dynamic area of financial Mathematics.
| 2 |
Author(s):
Awogbemi Clement Adeyeye.
Page No : 12-24
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On the Probability of Gambler’s Ruin System
Abstract
A typical Gambler’s ruin problem was considered in this work by applying theory of difference equations. The expected gains and duration of the game were generated for both fair and unfair games. In order to develop the probabilities that a Gambler meets the target of initial capital units, the frequency on steps hitting zero or initial capital was computed. As a particular unit tends to infinity, the sum of probabilities of ruin and success was established to be unity. Boundary conditions were set up to develop the generating function for the duration of the game. To ascertain these, the conditions were validated by finding the generating functions for probability of gambler’s ruin at zero and unit absorptions. The illustrated example showed that the expected gain is 0 when the game is fair and negative when it is unfair. While the expected duration of the game was found to be infinite for a fair game, an infinitely prolonged game series is infeasible.
| 3 |
Author(s):
Babatunde O.S., Oni O.V., Adenomon M.O., Abiola O.J., Folorunso G.A..
Page No : 25-36
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An Empirical Analysis of Unemployment and Inflation Rate in Nigeria
Abstract
Inflation distorts the working of the price system, creates arbitrary redistribution from debtors to creditors, disrupt productive investment activity, and it is usually costly to eliminate. Also, the inability of job seekers to secure gainful employment tends to create disaffection among people and causes the youth, to resort to social vices (such as robbery, suicide, prostitution, drug addiction, terrorism and political unrest etc. in Nigeria. Thus, this research used the Annual data on Unemployment and Inflation rate which were extracted from Central Bank of Nigeria (CBN) 2019 statistical bulletin to investigate the relationship between unemployment rate and inflation rate in Nigeria. Jarque-Bera normality test was first conducted on the variables which reveal that the variables are normally distributed. Unit root test was also carried out on the macroeconomic variables which the results revealed that all the variables are stationary at first difference. The existence of long run relationship was also investigated using Johansen and Juselius Cointegration Test. The trace test and the maximum eigenvalue test showed there exist long run relationship between unemployment rate and inflation rate in Nigeria. Also, VECM model was implemented; the results revealed that inflation rate and unemployment rate are significantly negatively related in the long run in Nigeria. Error Correction Model (ECM) was developed to study the short run dynamics of our variables, the pairwise Ganger causality test revealed that both variables do not Granger caused each other i.e. there is evidence of short run relationship between unemployment rate and inflation rate in Nigeria. For the short run models, a normality test was conducted using histogram on the residuals and evidence from the Jarque-Bera test revealed that the residuals are normally distributed (p-values>0.05). The CUSUM stability test shows that the parameters of the short run unemployment rate model are not stable over time while for inflation rate model, the parameters of the model are stable over time i.e. an increase in inflation rate leads to decrease in unemployment rate and on the other hand increase in unemployment rate leads to decrease in inflation rate in Nigeria. Thus, inflation rate does not granger cause unemployment rate in Nigeria and also unemployment rate does not granger cause inflation rate in Nigeria.
| 4 |
Author(s):
Etaga Harrison O., Etaga Cecilia N., Aforka Kenechukwu F., Nzonwa Theresa U..
Page No : 37-61
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Ratio Type Estimators Using the Linear Combination of Quartile Deviation and Population Deciles of Auxiliary Variable: A Comparative Analysis of Some Classes of Estimators
Abstract
Many ratio type estimators for population means are in vogue. Researchers, over the years, have been making efforts to improve the efficiency of these estimators. Year after year they introduce modified estimators which they claimed performed better than other ratio estimators in literature. There is need to carrying out empirical study to determine the best of these estimators, the circumstance at which it performs best; and also, to find out if the estimators are distribution sensitive, compared the estimator to ascertain if they are affected by sample size. A simulation study was carried out and the result showed that the tenth estimator is the most efficient of the twenty estimators considered; it performed better than others irrespective of the distribution of the study and auxiliary variables; and also, that the efficiency of the estimators increases as sample size increases.
| 5 |
Author(s):
Etaga Harrison O., Etaga Cecilia N., Aforka Kenechukwu F., Okeke Stella E..
Page No : 62-71
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Student Enrolment Pattern In Anambra State (2001 -2015)
Abstract
Primary and secondary schools. It has occurred that for the past years, people in Anambra state has been battling with lack of knowledge on the rate or pattern in which students in primary and secondary school enroll. And the rate at which male and female enroll in these institutions. It becomes necessary to determine the trend at which students enroll into primary and secondary schools in Anambra state in each of the Local Government Area. The data used for this work is secondary in nature. They were obtained from Anambra State Statistical Year Book from 2001 to 2015. The statistical methods used in data analysis are Trend analysis and student t-test. The data were tested for normality using Shapiro-Wilk test and the result showed that the date is normally distributed. Homogeneity of variance was also tested using Bartlet test and Levene test, data was found to be homogenous. Test of Independence, showed that the data set are independent. Trend Analysis was carried out using Least Square Method. The results showed that significant difference exists between the enrollment of the male and the female students in the state. Finally, that as eight states has increment in 2020 while thirteen states will have a decrement in the student’s enrollment in the year 2020. Special attention should be placed on this local government Area with decrement in their enrolment in 2020 to actually know why there the decrement exist.
| 6 |
Author(s):
Awogbemi Clement Adeyeye, Urama Kenny Ugochukwu.
Page No : 72-77
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On Probabilities of Misclassification Related to Logit-normal Distribution
Abstract
The probabilities of misclassification associated with logit-normal distribution are studied in this work by examining the logistic transformation on normally distributed random variables. The distribution theory and rules in respect of logit-normal distribution for conditional and expected probabilities of misclassification are also considered. While the probability density function (pdf) of conditional probability is generated, the expected probability of misclassification is approximately established.
