Swing Options Valuation: a BSDE with Constrained Jumps Approach

TL;DR

This paper introduces a novel probabilistic approach using BSDEs with constrained jumps to price Swing options, providing convergence analysis and numerical validation within the Black-Scholes model.

Contribution

The paper develops a new method for solving impulse control problems via BSDEs with constrained jumps, including a penalization scheme and convergence analysis.

Findings

Convergence rate of penalization error is established.

Numerical tests demonstrate the method's effectiveness.

Comparison with classical methods shows improved performance.

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.