BUILDING ARBITRAGE-FREE IMPLIED VOLATILITY: SINKHORN'S ALGORITHM AND VARIANTS

Hadrien de March (1) , Pierre Henry-Labordere (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 SOCIETE GENERALE - Equity Derivatives Research Societe Generale

We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently used to solve efficiently (martingale) optimal transport problems.

Domaines: Finance quantitative [q-fin.CP]

Hadrien de March, Pierre Henry-Labordere. BUILDING ARBITRAGE-FREE IMPLIED VOLATILITY: SINKHORN'S ALGORITHM AND VARIANTS. 2019. ⟨hal-02011533⟩