Pricing and Hedging Defaultable Claim

Stéphane Goutte (1) , Armand Ngoupeyou (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the pricing and the hedging of claim Ψ which depends of the default times of two firms A and B. In fact, we assume that we can not buy or sell any default- able bond from the firm B but we can trade a defaultable bond of the firm A. Since the default times of the two firms are correlated, our aim is to find the best price and hedg- ing of Ψ using bond of the firm A. Hence we solve this problem in two cases: first in a Markov framework using indifference price and solving a system of Hamilton Jacobi Bellman equation; and in a secondly in a more general framework (mean-variance tradeoff process non deterministic) using the mean variance hedging approach and solving backward stochastic differential equations.

Mots clés: Default and Credit risk; Hamilton Jacobi Bellman and Backward Differential equations; Mean variance hedging

Domaines: Probabilités [math.PR]

Stéphane Goutte, Armand Ngoupeyou. Pricing and Hedging Defaultable Claim. 2011. ⟨hal-00625265v1⟩