This is the first of two papers in which we consider a stock with price process defined by a stochastic differential equation driven by a process Y (·) different from Brownian motion. The adoption of such a colored noise input is motivated by an analysis of real market data. The process Y (·) is defined by a continuous-time AR(∞)-type equation and may have either short or long memory. We show t...

Using the Mellin transform a new method for solving the Black-Scholes equation is proposed. Our approach does not require either variable transformations or solving diffusion equations.

This paper revisits some solution methods for Black-Scholes equation and some of its nonlinear versions arising in option pricing theory.

The Black-Scholes Equation is arguably the most influential financial equation, as it an effective example of how to eliminate risk from a portfolio by using hedged position. Hedged positions are used many firms, mutual funds and finance companies increase value assets over time. derivation equation often considered difficult understand overly complicated, when in reality confusion arises misun...

In this paper, the Black–Scholes equation is solved using a new technique. This scheme derived by combining Laplace transform method and nonstandard finite difference (NSFD) strategy. The qualitative properties of are discussed, it shown that positive, stable, consistent when low volatility assumed. efficiency demonstrated numerical example.

Several techniques of fundamental physics like quantum mechanics, field theory and related tools of non-commutative probability, gauge theory, path integral etc. are being applied for pricing of contemporary financial products and for explaining various phenomena of financial markets like stock price patterns, critical crashes etc.. The cardinal contribution of physicists to the world of financ...