Journal of Computational Finance

Numerical techniques for the valuation of basket options and their Greeks

Corinna Hager, Stefan Hüeber, Barbara I. Wohlmuth


In this paper, an efficient approach for the computation of the fair value of a basket option as well as its Greeks is presented. Both European and American options are considered; the determination of the price of the former leads to the solution of a parabolic partial differential equation, whereas for the latter a variational inequality needs to be solved. The variational formulations are discretized in terms of finite differences in time and finite elements in space. By enforcing the inequality constraints of the American option via Lagrange multipliers, the discrete inequality can be reformulated as a set of semismooth equations that is solved in terms of a primal-dual active set strategy. In order to estimate the Greeks, we construct a piecewise multilinear interpolant of the pricing function with respect to the coefficients of the differential equation. The partial derivatives of this interpolant serve as an approximation of the Greeks that can thus be evaluated for any combination of assets and market parameters. The number of function evaluations necessary for the interpolation is reduced by using dimension-adaptive sparse grids for the discretization of the parameter space. Several numerical examples illustrate the robustness and applicability of the schemes.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here