A Fast Numerical Method for the Black--Scholes Equation of American Options

A Radial Point Interpolation Method for Pricing Options on a Dividend Paying Asset

“…for call (4) where N (·) is the cumulative distribution function of the standard normal distribution with…”

“…They defined an algorithm which is computationally efficient and guarantees to generate prices that exclude arbitrage possibilities. Some other relevant works that can be worth mentioning here are those of Khaliq et al [7] who developed adaptive θ-methods for solving the Black-Scholes PDE for American options; Zhao et al [17] who discussed some compact finite difference methods for pricing American options on a single asset with methods for dealing with optimal exercise boundary, and Tangman and Bhuruth [14] who described an improvement of Han and Wu's algorithm [4] for American options. The RPIM has the following advantages ( [9]): The shape function has the Kronecker delta property, which facilitates easy treatment of the essential boundary conditions; the moment matrix used in constructing shape functions is always invertible for irregular nodes; and the polynomials can be exactly reproduced up to desired order by polynomial augmentation.…”

Pricing American Put Option With Dividends on Variational Inequality

“…Based on results of domestic and foreign research in [6,7], this paper consider the numerical solution of the variational inequality model for American put option with dividends, deep in studying on the splitting method in time, obtained the numerical algorithm with dividends, and the experimental results show that this method is a very effective in solving the American put option pricing model, and the splitting method is better than finite difference method. …”

Path Averaged Option Value Criteria for Selecting Better Options

“…Beginning in 1973, it was described that a mathematical framework for finding the fair price of a European option by Black and Scholes [1,2], several numerical methods have been presented for the cases where analytic solutions are neither available nor easily computable. See more details about numerical methods such as finite difference method (FDM) [3,4,5,6,7,8,9,10,11,12,13], finite element method [14,15,16], finite volume method [17,18,19], and a fast Fourier transform [20,21,22,23,24]. For convenience, we use the closed-form of the Black-Scholes equation in this work.…”