Swing Options Valuation:a BSDE with Constrained Jumps Approach

Marie Bernhart (1, 2) , Huyên Pham (1, 3) , Peter Tankov (4) , Xavier Warin (2, 5)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 EDF - EDF
3 CREST - Centre de Recherche en Économie et Statistique
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
5 FiME Lab - Laboratoire de Finance des Marchés d'Energie

We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity $\lambda$, the penalization parameter $p > 0$ and the time step. In particular, we obtain a convergence rate of the error due to penalization of order $(\lambda p)^{\alpha - \frac{1}{2}}, \forall \alpha \in \left(0, \frac{1}{2}\right)$. Combining this approach with Monte Carlo techniques, we then work out the valuation problem of (normalized) Swing options in the Black and Scholes framework. We present numerical tests and compare our results with a classical iteration method.

Mots clés: Backward stochastic differential equations with constrained jumps; Impulse control problems; Swing options; Monte Carlo methods

Domaines: Finance quantitative [q-fin.CP]

Marie Bernhart, Huyên Pham, Peter Tankov, Xavier Warin. Swing Options Valuation:a BSDE with Constrained Jumps Approach. 2011. ⟨hal-00553356⟩