Stochastic Evolution of Distributions - Applications to CDS indices

Guillaume Bernis (1) , Nicolas Brunel (2) , Antoine Kornprobst (3, 4) , Simone Scotti (5)

1 Natixis Asset Management
2 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
3 CES - Centre d'économie de la Sorbonne
4 Labex ReFi
5 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We use mixture of percentile functions to model credit spread evolution, which allows to obtain a flexible description of credit indices and their components at the same time. We show regularity results in order to extend mixture percentile to the dynamic case. We characterise the stochastic differential equation of the flow of cumulative distribution function and we link it with the ordered list of the components of the credit index. The main application is to introduce a functional version of Bollinger bands. The crossing of bands by the spread is associated with a trading signal. Finally, we show the richness of the signals produced by functional Bollinger bands compared with standard one with a pratical example.

Mots clés: Mathematical Methods; Model Construction and Validation; Stochastic Analysis; Credit Default Swaps; Dynamic Distributions

Domaines: Economies et finances; Probabilités [math.PR]

Guillaume Bernis, Nicolas Brunel, Antoine Kornprobst, Simone Scotti. Stochastic Evolution of Distributions - Applications to CDS indices. 2017. ⟨halshs-01467736⟩