Journal of Computational Finance

Risk.net

Efficient conservative second-order central-upwind schemes for option-pricing problems

Omishwary Bhatoo, Arshad Ahmud Iqbal Peer, Eitan Tadmor, Désiré Yannick Tangman and Aslam Aly El Faidal Saib

  • Option pricing using fully vectorised second-order central-upwind `"Black-Box''.
  • The efficient approach is extended to American, barrier, butterfly and digital options.
  • Fast, non-oscillatory and high-resolution numerical solutions and Greeks are obtained.

The conservative Kurganov–Tadmor (KT) scheme has been successfully applied to option-pricing problems by Germán I. Ramírez-Espinoza and Matthias Ehrhardt. These included the valuation  of European, Asian and nonlinear  options as Black–Scholes partial differential  equations, written in the conservative form, by simply updating fluxes in the black box approach. In this paper, we describe an improvement of this idea through a fully vectorized algorithm of nonoscillatory slope limiters and the efficient use of time solvers. We also propose the application of second-order extensions of KT to option-pricing problems. Our test problems solve one-dimensional benchmark and convection-dominated  European options  as well as digital and butterfly options.  These demonstrate the robustness and flexibility of the pricing methods and set a basis for complex problems. Further, the computation of option Greeks ensures the reliability of these methods. Numerical experiments are performed on barrier options, early exercisable American options and two-dimensional fixed and floating strike Asian options. To the authors’ knowledge, this is the first time American options have been priced by applying the early exercise condition on the semi-discrete formulation of central-upwind schemes. Our results show second-order, nonoscillatory and high-resolution properties of the schemes as well as computational efficiency.

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 Risk.net? View our subscription options

You need to sign in to use this feature. If you don’t have a Risk.net 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