TY - JOUR
T1 - Modelling and Numerical Valuation of Power Derivatives in Energy Markets
AU - Nguyen , Mai Huong
AU - Ehrhardt , Matthias
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 259
EP - 293
PY - 2012
DA - 2012/04
SN - 4
DO - http://doi.org/10.4208/aamm.10-m1133
UR - https://global-sci.org/intro/article_detail/aamm/119.html
KW - Swing options, jump-diffusion process, mean-reverting, Black-Scholes equation,
energy market, partial integro-differential equation, theta-method, Implicit-Explicit-Scheme.
AB - <p style="text-align: justify;">In this work we investigate the pricing of swing options in a model
where the underlying asset follows a jump diffusion process. We focus on the
derivation of the partial integro-differential equation (PIDE) which will be applied
to swing contracts and construct a novel pay-off function from a tree-based pay-off
matrix that can be used as initial condition in the PIDE formulation. For valuing
swing type derivatives we develop a theta implicit-explicit finite difference scheme
to discretize the PIDE using a Gaussian quadrature method for the integral part.
Based on known results for the classical theta-method the existence and uniqueness
of solution to the new implicit-explicit finite difference method is proven. Various
numerical examples illustrate the usability of the proposed method and allow us
to analyse the sensitivity of swing options with respect to model parameters. In
particular, the effects of number of exercise rights, jump intensities and dividend
yields will be investigated in depth.</p>