##### Analytical Solution of Black-Scholes Equation in Predicting Market Prices and Its Pricing Bias

Azor, Promise Andaowei, Amadi, Innocent Uchenna

Asian Journal of Probability and Statistics, Page 17-23
DOI: 10.9734/ajpas/2020/v8i230202

This paper is geared towards implementation of Black-Scholes equation in valuation of European call option and predicting market prices for option traders. First, we explained how Black-Scholes equation can be used to estimate option prices and then we also estimated the BS pricing bias from where market prices were predicted. From the results, it was discovered that Black-Scholes values were relatively close to market prices but a little increase in strike prices (K) decreases the option prices. Furthermore, goodness of fit test was done using Kolmogorov –Sminorvov to study BSM and Market prices.

##### Aspects of Modern Systemic Approach (III): Implications of Random Processes in the Study of Dynamic Systems

Bogdan-Vasile Cioruța

Asian Journal of Probability and Statistics, Page 24-48
DOI: 10.9734/ajpas/2020/v8i230203

The purpose of this study is to familiarize the reader with the diversity of concepts (notions) and stages of development specific to Probability Theory, with the definition and characterization of variables, vectors and random processes, respectively with the most important elements that give random processes. Among these we mention the distribution function, the probability density function, the statistical moments of a random process, the temporal averages, and respectively the correlation (and intercorrelation) of a random signal (process). Also, the implications of random processes in the study of dynamical systems are reviewed, as well as a series of applications specific to the analysis of dynamic behavior.

##### The Inverse Lomax-G Family with application to Breaking Strength Data

Jamilu Yunusa Falgore, Sani Ibrahim Doguwa

Asian Journal of Probability and Statistics, Page 49-60
DOI: 10.9734/ajpas/2020/v8i230204

We proposed a new class of distributions with two additional positive parameters called the Inverse Lomax-G (IL-G) class. A special case was discussed, by taking Weibull as a baseline. Different properties of the new family that hold for any type of baseline model are derived including moments, moment generating function, entropy for Renyi, entropy for Shanon, and order statistics. The performances of the maximum likelihood estimates of the parameters of the sub-model of the Inverse Lomax-G family were evaluated through a simulation study. Application of the sub-model to the Breaking strength data clearly showed its superiority over
the other competing models.

##### A Study on Second Order Rotatable Designs under Tri-diagonal Correlated Structure of Errors Using a Pair of Balanced Incomplete Block Designs

K. Raghavendra Swamy, B. Re. Victorbabu

Asian Journal of Probability and Statistics, Page 61-74
DOI: 10.9734/ajpas/2020/v8i230205

In this paper, a study on second order rotatable designs under tri-diagonal correlated structure of errors using a pair of balanced incomplete block designs is suggested. Further, the variance function of the estimated response for different values of tri-diagonal correlated coefficient and distance from centre  for  ( - factors) are studied.

##### A Critique on the Foundational Response Surface Methodology for Exploring Optimal Regions

John E. Usen, Essien J. Okoi, Eric M. Egomo, Ekeng N. Henshaw, Edet B. Hogan

Asian Journal of Probability and Statistics, Page 1-16
DOI: 10.9734/ajpas/2020/v8i230201

The interest of most process engineers in industries is usually to optimize the yield of their processes. Not until 1951, imprecise methodologies were used in industries for this purpose. However, in 1951, G. E. P. Box and K. B. Wilson invented the technique of Response Surface Methodology (RSM) as one used for the optimization of the yield of processes. Being an initial idea, this paper has considered RSM as a foundational idea. In particular, it criticizes this foundational idea from the angle of its intuitive approach to searching for near-optimal settings of industrial processes, should such processes fail to run at optimal settings. RSM uses the tools of canonical transformation and analysis (a trial-and-error routine) for this search. Regardless, the foundational response surface methodology is acknowledged to be primarily efficient for determining the optimum response.