Analysis of the stability of the linear boundary condition for the Black–Scholes equation

Abstract

Abstract. The linear asymptotic boundary condition, i.e. assuming that the second derivative of the value of the derivative security vanishes as the asset price becomes large, is commonly used in practice. To our knowledge, there have been no rigorous studies of the stability of these methods, despite the fact that the discrete matrix equations obtained using this boundary condition loses diagonal dominance for large timesteps. In this paper, we demonstrate that the discrete equations obtained using this boundary condition satisfy necessary conditions for stability for a finite difference discretization. Computational experiments also show that this boundary condition satisfies sufficient conditions for stability as well.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 118 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.