We present a method of deriving analytical solutions for two-dimensional Black-Scholes-Merton equation. The consists three changes variables in order to reduce the original partial differential equation (PDE) normal form and then solve it. Analytical two cases option pricing on minimum maximum assets are derived using our shown agree with previously published results. advantage solution procedu...

Financial theory can incorporate fractional differential equation, which provides new concepts and methods for theoret- ical analysis practical implementations. In this research, a numerical method to solve time Black-Scholes European option pricing model is developed applied using extended cubic B-spline Caputo derivative. The graphical results shows that the prices from proposed technique agr...

We introduce a new class of strategies for hedging derivative securities in the presence of transaction costs assuming lognormal continuous time prices for the underlying asset We do not assume necessarily that the payo is convex as in Leland or that transaction costs are small compared to the price changes between portfolio adjustments as in Hoggard Whalley and Wilmott The type of hedging stra...

in this paper, we try and valuate preemption rights by modifying the black-scholes model, which is widely used to valuate options and other derivatives. here we first present the basics of the black-scholes model and then we discus modification of the model to be fit for preemption right valuation. at the end, we valuate four of the preemptive rights using the proposed model