The equity option volatility smile: an implicit finite-difference approach

Abstract

ABSTRACT This paper illustrates how to construct an unconditionally stable finite-difference lattice consistent with the equity option volatility smile. In particular, the paper shows how to extend the method of forward induction on Arrow-Debreu securities to generate local instantaneous volatilities in implicit and semi-implicit (Crank-Nicholson) lattices. The technique developed in the paper provides a highly accurate fit to the entire volatility smile and offers excellent convergence properties and high flexibility of asset- and time-space partitioning. Contrary to standard algorithms based on binomial trees, our approach is well suited to price options with discontinuous payouts (e.g. knock-out and barrier options) and does not suffer from problems arising from negative branching probabilities.

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 — 199 citations exist upstream.