In this paper, we studied the particular cases of higher-order realized multipower variation process, their asymptotic properties comprising the probability limits and limit distributions were highlighted. The respective asymptotic variances of the limit distributions were obtained and jump detection models were developed from the asymptotic results. The models were obtained from the particular cases of the higher-order of the realized multipower variation process, in a class of continuous stochastic volatility semimartingale process. These are extensions of the method of jump detection by Barndorff-Nielsen and Shephard (2006), for large discrete data. An Empirical Application of the models to the Nigerian All Share Index (NASI) data shows that the models are robust to jumps and suggest that stochastic models with added jump components will give a better representation of the NASI price process.

We examine empirically, the suitability of three stock price models viz: geometric Brownian motion, symmetric and asymmetric jump-diffusion models, on the empirical log-returns of the Nigerian All-Share Index. 5334 daily observed data from January 2, 1998, to February 21, 2020, were utilized. Using a non-parametric jump-test method, our results show that jumps are present in the empirical log-returns of the stock market price. The results obtained for the optimal parameters in the models indicate high jump intensity, more upward jumps, and a positively skewed jump process. However, the parameters in the asymmetric jump-diffusion model were found to be more sensitive to the varied threshold of jumps in the log-returns than the symmetric jump-diffusion model. The suitability analysis results show that the symmetric jump-diffusion model fits the market indices better. Therefore, it can be used for future predictions of the market price.

In this paper, a generalized jump-diffusion process driven by the Asymmetric Laplace (AL) Distribution for stock price modeling was proposed. The probability density function was derived for the dynamics of the log-returns when the random process of the jump amplitude obeys the AL distribution. Based on the derived density function, a Lévy-Khintchine formula for the process was obtained, which proved useful for the computation of moments of the process. Hence, the Asymmetric Laplace jump diffusion model can be useful for modelling of stock price processes with empirical features like discontinuous paths, asymmetry and high peaks found in the empirical distribution of most financial data.

In this paper, a compartmental model for the transmission dynamics of the new infectious disease referred to as COVID-19 is employed. The model comprises five mutually exclusive compartments (classes) of human population sizes viz: susceptible, exposed, infected, recovered, and death, representing the human dynamics; hence, the name SEIRD model. In the model, the temporal dynamics of the COVID-19 outbreak in Nigeria and Spain are analyzed. The period is between February 15-April 3, 2020 for Spain, and February 27-April 3, 2020, for Nigeria. The analysis of the population data is based on the concerned SEIRD model. Graphical representations of the obtained results are presented. A connection between the contact rate of the infection and the compartmental human population sizes subject to the COVID-19 analysis is revealed. It shows that a decrease in the contact rate of the ‘susceptible and the infected’ classes is a considerable condition leading to a decline in 'the exposed, infected, and death' cases. This decrease is attributed to the control of the possible infecting contacts. The spread patterns for the two considered cases are the same. A lot of measures are needed to be put in place to ensure a corresponding increase in the 'recovered class.' The COVID-19 outbreak would remain global and endemic if the infecting contact rate is not well controlled. Thus, adherence to strict public and government policies such as social distancing and isolation is a plausible requirement. For other aspects of epidemiology with related features, this strategy is highly recommended for implementation.

In the Nigeria economy, cocoa production has been of great importance. This buttresses the fact that cocoa as a product is the leading agricultural export of Nigeria, leaving the country currently as the world fourth largest producer of cocoa, after Ivory Coast, Indonesia and Ghana and the third largest exporter, after Ivory Coast and Ghana. Hence, there is need for the agricultural sector expansion, effective predictive models and reliable price mechanism. This article examines tonnes of cocoa production dataset of the Nigeria agricultural sector for the period of twenty-four (24) years spanning between 1993 to 2016. The Correlation dynamics examined includes the autocorrelation features as affected by the production rate within the considered time interval. The degree of similarity between the dataset and the corresponding lagged version of itself over successive time interval is measured using a serial correlation test while the results mostly favour negative correlation showing that large current values correspond to small values at the specified lag. These dataset can effectively serve as good candidate for agricultural product modelling in terms of forecasting.

In this paper, stock price basic parameters: expected value and volatility are being estimated in the sense of Ito stochastic dynamics. For model efficiency, stock exchange data of DBS Group Holding Ltd (D05. SI) spanning between May 23, 2010 to May 15, 2016 (weekly data with 312 sample size) are considered. It is remarked that the data, and the proposed models have many applications in financial institutions, and other areas of applied sciences. AMS Subject Classification: 91B25, 93E35

The Variance-Gamma (VG) process is a three parameter stochastic process with respect to a Brownian motion. Here, we consider in our presentation, a detailed study of the VG process expressed as a difference of two gamma processes. As a result, we obtain the basic moments of the process using the characteristic function of the VG process with regard to the parameters of a differenced gamma processes. Also, the Levy-Khintchine formula for the process is derived via the Frullani’s integral. Finally, a modified European call option VG model incorporating a difference of two gamma processes is proposed.

In quantitative finance and option pricing, one of the basic determinants of option prices is the volatility of the underlying asset. In this paper, we therefore, present a concise study of volatility in option pricing in the sense of Dupire’s approach. Thereafter, we outspread such study via the application of Ito formula to the modelling and valuation of currency option with local volatility. For the purpose of efficiency, we use the daily historical prices of stock-S&P 500 for a certain period to estimate the corresponding historical volatility. Graphical representation of the analysed daily historical data of stock prices with respect to a local volatility is presented.

In this paper, observer design in generalized state space also known as singular system of transistor circuits is solved using the Differential transform method (DTM) and the Picard iterative technique (PIT). The numerical results obtained via these methods converge rapidly to their associated exact solutions upon comparison. It is obvious that these results are in excellent agreement with those already in literature via other numerical methods. However, the DTM reveals the ease of application and fewer computations compared to other numerical methods. Whereas, the PIT requires the Lipschitzian continuity condition to be satisfied.

This paper introduces a new probability distribution referred to as a transformed triangular distribution (TTD) by using the average of the extreme values (minimum and maximum) of the triangular distribution. The TTD is being approximated by the continuous uniform distribution. The basic moments of the TTD and those of the continuous uniform distribution are compared respectively, and a relationship established. This can be used in modeling and simulation.

In this paper, stochastic analysis of the behaviour of stock prices is considered using a proposed log- normal distribution model. To test this model, stock prices for a period of 19 years were taken from the Nigerian Stock Exchange (NSE) for simulation, and the results reveal that the proposed model is efficient for the prediction of stock prices. Better accuracy of results via this model can be improved upon when the drift and the volatility parameters are structured as stochastic functions of time instead of constants parameters.