On Duality Principle in Exponentially Lévy Market

This paper describes the effect of duality principle in option pricing driven by exponentially Lévy market model. This model is basically incomplete - that is; perfect replications or hedging strategies do not exist for all relevant contingent claims and we use the duality principle to show the coincidence of the associated underlying asset price process with its corresponding dual process. The condition for the ‘unboundedness’ of the underlying asset price process and that of its dual is also established. The results are not only important in Financial Engineering but also from mathematical point of view

Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method

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

ON A DIVIDEND-PAYING STOCK OPTIONS PRICING MODEL (SOPM) USING CONSTANT ELASTICITY OF VARIANCE STOCHASTIC DYNAMICS

In this paper, we propose a pricing model for stock option valuation. The model is derived from the classical Black-Scholes option pricing equation via the application of the constant elasticity of variance (CEV) model with dividend yield. This modifies the Black- Scholes equation by incorporating a non-constant volatility power function of the underlying stock price, and a dividend yield parameter

Stochastic Analysis of Stock Market Price Models: A Case Study of the Nigerian Stock Exchange (NSE)

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

Understanding How Dividends Affect Option Prices

In this paper, we propose a pricing model for stock option valuation. The model is derived from the classical Black-Scholes option pricing equation via the application of the constant elasticity of variance (CEV) model with dividend yield. This modifies the Black- Scholes equation by incorporating a non-constant volatility power function of the underlying stock price, and a dividend yield parameter

He’s Polynomials for Analytical Solutions of the Black-Scholes Pricing Model for Stock Option Valuation

The Black-Scholes model is one of the most famous and useful models for option valuation as regards option pricing theory. In this paper, we propose a semianalytical method referred to as He’s polynomials for solving the classical Black-Scholes pricing model with stock as the underlying asset. The proposed method gives the exact solution of the solved problem in a very simple and quick manner even with less computational work while still maintaining high level of accuracy. Hence, we recommend an extension and adoption of this method for solving problems arising in other areas of financial engineering, finance, and applied science

A Note on Black-Scholes Pricing Model for Theoretical Values of Stock Options

In this paper, we consider some conditions that transform the classical Black-Scholes Model for stock options valuation from its partial differential equation (PDE) form to an equivalent ordinary differential equation (ODE) form. In addition, we propose a relatively new semi-analytical method for the solution of the transformed Black-Scholes model. The obtained solutions via this method can be used to find the theoretical values of the stock options in relation to their fair prices. In considering the reliability and efficiency of the models, we test some cases and the results are in good agreement with the exact solution

The Modified Black-Scholes Model via Constant Elasticity of Variance for Stock Options Valuation

In this paper, the classical Black-Scholes option pricing model is visited. We present a modified version of the Black-Scholes model via the application of the constant elasticity of variance model (CEVM); in this case, the volatility of the stock price is shown to be a non-constant function unlike the assumption of the classical Black-Scholes model