This paper presents a convergence analysis of Crank–Nicolson and Rannacher time-marching methods which are often used in finite difference discretizations of the Black–Scholes equations. Particular attention is paid to the important role of Rannacher’s startup procedure, in which one or more initial timesteps use backward Euler timestepping, to achieve second-order convergence for approximation...

In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thomée (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally parallelizable. It is shown that the method is very efficient for calculating various option prices. Existence and uniqueness properties of the Laplace transfo...

This article develops an option pricing model to evaluate knowledge management (KM) activities from the following perspectives: knowledge creation, knowledge conversion, knowledge circulation, and knowledge carry out. This paper makes three important contributions: (1) it provides a formal theoretical grounding for the validity of the Black-Scholes model that might be employed to KM; (2) it pro...

Following an approach introduced by Lagnado and Osher (1997), we study Tikhonov regularization applied to an inverse problem important in mathematical finance, that of calibrating, in a generalized Black–Scholes model, a local volatility function from observed vanilla option prices. We first establish W 1,2 p estimates for the Black–Scholes and Dupire equations with measurable ingredients. Appl...

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 discusses the generalized Black-Scholes-Merton model, where volatility coefficient, drift coefficient of stocks, and interest rate are time-dependent deterministic functions. Together with it, we make assumption that volatility, drift, depend on a gamma or inverse-gamma random variable. model includes models skew Student’s t- variance-gamma-distributed stock log-returns. The price Eu...