Ricerca rapida

The Black-Scholes Equation

Application ID: 82


The Black-Scholes equation, computes the value u of a European stock option. Black-Scholes derived an analytical expression for the solution to this problem. However, the formula works only for certain cases; for instance, you cannot employ it when sigma and r are functions of x and t. Here, sigma denotes the volatility, r the continuous compounding rate of interest, and x the underlying asset price.

Using a PDE formulation allows you to determine the price for such cases. This model sets up the PDE formulation of the Black Scholes equation and in addition, this model also shows how to solve the 1D time-dependent variation using a 2D geometry with the y-coordinate corresponding to time.

Questo modello è stato realizzato con:

COMSOL Multiphysics®

The combination of COMSOL® products required to model your application depends on the physics interfaces that define it. Particular physics interfaces may be common to several products (see the Specification Chart for more details). To determine the right combination of products for your project, you should evaluate all of your needs in light of each product\'s capabilities, consultation with the COMSOL Sales and Support teams, and the use of an evaluation license.