Determining the implied volatility in the Dupire equation for vanilla European call options

Mourad Bellassoued (1) , Raymond Brummelhuis (2) , Michel Cristofol (3) , Eric Soccorsi (4)

1 Faculté des Sciences de Bizerte [Université de Carthage]
2 LMR - Laboratoire de Mathématiques de Reims
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités
4 CPT - Centre de Physique Théorique - UMR 7332

The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a collection of quoted option prices with different strikes.

Mots clés: Inverse problem; Black-Scholes model; Dupire equation; implied volatility

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Bellassoued, Raymond Brummelhuis, Michel Cristofol, Eric Soccorsi. Determining the implied volatility in the Dupire equation for vanilla European call options. 2013. ⟨hal-00782927v3⟩