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Swing Options Valuation:a BSDE with Constrained Jumps Approach

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

(2011-01)

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.

1:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
2:	EDF R&D
	EDF
3:	Centre de Recherche en Économie et Statistique (CREST)
	INSEE – École Nationale de la Statistique et de l'Administration Économique
4:	Centre de Mathématiques Appliquées (CMAP)
	Ecole Polytechnique
5:	Laboratoire de Finance des Marchés d'Energie (FiME Lab)
	Université Paris IX - Paris Dauphine – CREST – EDF R&D

Subject

:

Quantitative Finance/Computational Finance

Keyword(s): Backward stochastic differential equations with constrained jumps – Impulse control problems – Swing options – Monte Carlo methods

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From: Marie Bernhart <>

Submitted on: Friday, 7 January 2011 11:46:49

Updated on: Friday, 7 January 2011 14:15:21