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Jump-diffusion models with two stochastic factors for pricing swing options in electricity markets with partial-integro differential equations.

Authors :
Calvo-Garrido, M. Carmen
Ehrhardt, Matthias
Vázquez, Carlos
Source :
Applied Numerical Mathematics. May2019, Vol. 139, p77-92. 16p.
Publication Year :
2019

Abstract

Abstract In this paper we consider the valuation of swing options with the possibility of incorporating spikes in the underlying electricity price. This kind of contracts are modelled as path dependent options with multiple exercise rights. From the mathematical point of view the valuation of these products is posed as a sequence of free boundary problems where two consecutive exercise rights are separated by a time period. Due to the presence of jumps, the complementarity problems are associated with a partial-integro differential operator. 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 of the operator, 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. In addition, we use an augmented Lagrangian active set method to cope with the early exercise feature. Moreover, we employ appropriate artificial boundary conditions to treat the unbounded domain numerically. Finally, we present some numerical results in order to illustrate the proper behaviour of the numerical schemes. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01689274
Volume :
139
Database :
Academic Search Index
Journal :
Applied Numerical Mathematics
Publication Type :
Academic Journal
Accession number :
134733614
Full Text :
https://doi.org/10.1016/j.apnum.2019.01.001