Journal of Computational Finance

Risk.net

Path-dependent American options

Etienne Chevalier, Vathana Ly Vath and Mohamed Mnif

  • In this paper, we investigate a path-dependent American option problem and provide an efficient and implementable numerical scheme for the solution of its associated path-dependent variational inequality.
  • We obtain the viscosity characterization of our value function and suggest a monotone, stable and consistent numerical scheme, the convergence of which is proven thanks to the uniqueness property.
  • We further enrich our study by providing and implementing a numerical algorithm. Some numerical results are also included.

In this paper, we investigate a path-dependent American option problem and provide an efficient and implementable numerical scheme for the solution of its associated path-dependent variational inequality.We obtain the viscosity characterization of our value function and suggest a monotone, stable and consistent numerical scheme, the convergence of which is proven thanks to the uniqueness property.We further enrich our study by providing and implementing a numerical algorithm. Some numerical results are also included.

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