Jump-diffusion models with two stochastic factors for pricing swing options in electricity markets with partial-integro differential equations
Use this link to cite
http://hdl.handle.net/2183/35195
Except where otherwise noted, this item's license is described as Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC-BY-NC-ND)
Collections
- GI-M2NICA - Artigos [75]
Metadata
Show full item recordTitle
Jump-diffusion models with two stochastic factors for pricing swing options in electricity markets with partial-integro differential equationsDate
2019Citation
Calvo-Garrido, M. C., Ehrhardt, M., & Vázquez, C. (2019). Jump-diffusion models with two stochastic factors for pricing swing options in electricity markets with partial-integro differential equations. Applied Numerical Mathematics, 139, 77-92. https://doi.org/10.1016/j.apnum.2019.01.001
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.
Keywords
Swing options
Electricity price
Jump-diffusion models
Augmented Lagrangian Active Set (ALAS) formulation
Semi-Lagrangian method
Biquadratic Lagrange finite elements
Artificial boundary conditions
Electricity price
Jump-diffusion models
Augmented Lagrangian Active Set (ALAS) formulation
Semi-Lagrangian method
Biquadratic Lagrange finite elements
Artificial boundary conditions
Editor version
Rights
Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC-BY-NC-ND) © 2019 IMACS. Published by Elsevier B.V. All rights reserved.