A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

Céline Labart (1) , Jérôme Lelong (2, 3)

1 LAMA - Laboratoire de Mathématiques
2 MATHFI - Financial mathematics
3 MATHFI - Mathématiques financières

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementation

Mots clés: American options; local volatility model; non linear PDE; Monte-Carlo methods; parallel computing; backward stochastic differential equations

Domaines: Probabilités [math.PR]; Calcul parallèle, distribué et partagé [cs.DC]; Finance quantitative [q-fin.CP]; Pricing [q-fin.PR]

Céline Labart, Jérôme Lelong. A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options. [Research Report] LAMA-LJK. 2011. ⟨hal-00567729⟩