A backward dual representation for the quantile hedging of Bermudan options

Bruno Bouchard (1, 2) , Jean-François Chassagneux (3) , Géraldine Bouveret (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CREST - Centre de Recherche en Économie et Statistique
3 Imperial College London

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of the pricing function. This algorithm is similar to the usual American backward induction, except that it requires two additional Fenchel transformations at each exercise date. We provide numerical illustrations.

Mots clés: Bermudan options; stochastic target problems; quantile hedging

Domaines: Probabilités [math.PR]; Pricing [q-fin.PR]; Finance quantitative [q-fin.CP]

Bruno Bouchard, Jean-François Chassagneux, Géraldine Bouveret. A backward dual representation for the quantile hedging of Bermudan options. SIAM Journal on Financial Mathematics, 2016, 7 (1), pp.215-235. ⟨hal-01069270v2⟩