The Operator Splitting Method for Black-Scholes Equation

The use of iterative methods for solving Black-Scholes equation

The Black-Scholes Equation

The most important application of the Itô calculus, derived from the Itô lemma, in financial mathematics is the pricing of options. The most famous result in this area is the Black-Scholes formulae for pricing European vanilla call and put options. As a consequence of the formulae, both in theoretical and practical applications, Robert Merton and Myron Scholes were awarded the Nobel Prize for E...

A new direct method for solving the Black-Scholes equation

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.

Laplace Transformation Method for the Black-scholes Equation

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...

Revisiting Black-Scholes Equation

In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships among the securities in the asset market. In special case where the interest ...