Swing Options Valuation:a BSDE with Constrained Jumps Approach

Abstract : 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2011

https://hal.archives-ouvertes.fr/hal-00553356
Contributeur : Marie Bernhart <>
Soumis le : vendredi 7 janvier 2011 - 11:46:49
Dernière modification le : vendredi 10 février 2017 - 01:13:12
Document(s) archivé(s) le : jeudi 30 juin 2011 - 13:12:37

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SWING_CJBSDE.pdf
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• HAL Id : hal-00553356, version 1

Citation

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

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