Crank-Nicolson Finite Difference Method with Sobolev Space Energy Estimate Theorem for Capital Market Prices

In this study, we have Black-Scholes analytic formula and Crank- Nicolson (CN) finite difference method for valuation of European put option which has earned the interests of researchers for determining both analytic and approximate solutions to Partial Differential Equations (PDEs) with Sobolev space energy estimate theorem. The simulations of analytical and numerical were effectively carried out. The results showed as follows: increase in volatility increases the values of option for both BS and CN prices, there are significant difference between BS and CN due to the changes of stock volatility, a little increase in the initial stock prices significantly increases the value of put option, when the strike price is greater than the initial stock price it increases put option values, Sobolev space energy estimates were used as asset value function to estimate asset prices at different maturity periods. Finally, the graphical solutions and comparisons of other parameters were discussed all in this paper which is informative to investors for the proper investment plans

Robust Methods of Assessing Fidelity Bank Share Price Movements in Nigeria Stock Market

Markov chain is a viable tool for studying the share price formation; since each finite state communicates for proper management decisions in Fidelity bank. Therefore, this paper studied stochastic analysis of Markov chain and PCA in the closing share price data of Fidelity (2016-2022) in Nigeria Stock Exchange. The share prices were transformed into 3-steps transition probability matrix solution to cover this number of years. The future share prices changes were known. The criteria of obtaining four share prices which formed 2x2 matrices were given and analytical solution of principal component were considered for future stock price changes. From the solution matrix of stochastic analysis, showed that Fidelity bank, PLC has the best probability of price increasing in the near future: 10%, best probability of reducing in future by 23% and best probability of no-change in the near future by 22% which is a tool for proper decision making in the day-to-day management of the bank; which shows it is profit making organization and are hopeful for future investment plans both short or long term respectively