Abstract: In this work we consider the valuation of swing options with the possibility of incorporating spikes in the underlying electricity price. These contracts are modelled as path dependent options with multiple exercise rights. From the mathematical point of view the valuation is posed in terms of a sequence of free boundary problems, where two exercise rights must be separated by a time period. Due to the presence of jumps, the complementarity problems are associated with a partial-integro differential operators. In order to solve the pricing problem, we propose appropriate numerical methods based on a Crank-Nicolson semi-Lagrangian method for the time discretization of the differential part jointly with the explicit treatment of the integral term by using the Adams-Bashforth scheme and combined with biquadratic Lagrange finite elements for space discretization. Additionally, we use an augmented Lagrangian active set method to cope with the early exercise feature when it appears. Moreover, we employ appropriate artificial boundary conditions to treat the bounded domain after truncation. We present some numerical results in order to illustrate the proper behaviour of the numerical schemes. This is a joint work with M.C. Calvo-Garrido and M. Ehrhardt