In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM) resulting from the modification of the classical Differential Transformation Method (DTM) is applied, for the first time, to the Black–Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed results represent the analytical values of the associated European call options, and the same algorithm can be followed for European put options. It is shown that PDTM is more efficient, reliable and better than the classical DTM and other semi-analytical methods since less computational work is involved. Hence, it is strongly recommended for both linear and nonlinear stochastic differential equations (SDEs) encountered in financial mathematics.

Predicting the future of a stock price is a difficult task due to the high level of randomness in the movement of prices. This research aims to use a machine-learning algorithm to estimate the closing stock price of a dataset to help aid in the prediction of stock prices leading to higher accuracy in prediction. The intention of the model is for it to be used as a day trading guide. The algorithm being used is called the least-squares linear regression model. It takes in a dependent variable, in this case, would be our closing price of the stock and an independent variable, which is the day each stock price was recorded.

In this paper, we consider a viable semi-analytical approach for the approximate-analytical solutions of certain system of functional differential equations (SFDEs) engendered by proportional delays. The proposed semi-analytical technique is built on the basis of the classical Differential Transform Method (DTM). The effectiveness and robustness of the proposed technique is illustratively demonstrated and the results are compared with their exact forms. We note also that using this method, the SFDEs with proportional delays need not be converted to SFDEs with constant delays before obtaining their solutions, and no symbolic calculation or initial guesstimates are required.

In this paper, a proposed semi-analytical method referred to as modified transformation Method resulting from the modification of the classical Differential Transformation Method (DTM) is applied to linear Schrödinger Equations. The results obtained converge faster to their exact forms. Illustrative examples are used and the results show that this modified version is very efficient, reliable and better than the classical DTM and other semi-analytical methods, as less computational work is involved. Hence, it is strongly recommended for both linear and nonlinear partial differential equations (PDEs) and stochastic differential equations (SDEs).

The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions are in good agreement with those of Rogers & Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani & Ahmad (ScienceAsia, 39S: 2013, 67–69). The proposed method is highly recommended for analytical solution of other forms of Asian option pricing models such as the geometric put and call options, even in their time-fractional forms. The basic Greeks obtained are the Theta, Delta, Speed, and Gamma which will be of great help to financial practitioners and traders in terms of hedging and strategy.

Contents IJPAM: Volume 107, No. 2 (2016)