# 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.
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Cited literature [25 references]

https://hal.archives-ouvertes.fr/hal-00553356
Contributor : Marie Bernhart <>
Submitted on : Friday, January 7, 2011 - 11:46:49 AM
Last modification on : Wednesday, May 15, 2019 - 3:40:18 AM
Long-term archiving on: Thursday, June 30, 2011 - 1:12:37 PM

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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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