Swing options valuation: a BSDE with constrained jumps approach.(English)Zbl 1247.91179

Carmona, René A. (ed.) et al., Numerical methods in finance. Selected papers based on the presentations at the workshop, Bordeaux, France, June 2010. Berlin: Springer (ISBN 978-3-642-25745-2/hbk; 978-3-642-25746-9/ebook). Springer Proceedings in Mathematics 12, 379-400 (2012).
Summary: 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 $$(\lambda p^{\alpha-\frac{1}{2}}, \forall \alpha \in (0, \frac {1}{2})$$. 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.
For the entire collection see [Zbl 1238.91005].

MSC:

 91G20 Derivative securities (option pricing, hedging, etc.) 91G99 Actuarial science and mathematical finance 60H30 Applications of stochastic analysis (to PDEs, etc.)
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