Modelling and Numerical Valuation of Power Derivatives in Energy Markets

Abstract

Abstract. 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.

A Kalman filtering approach to the detection of option mispricing in electric power markets

“…This approach gives flexibility to the quantity of electric energy to be purchased or delivered [1][2][3][4][5]. A minimum amount of and a maximum amount of energy is delivered for each swing action time, while for the whole contract period the overall minimum and maximum amount of energy are denoted as and respectively.…”

“…These schemes aim at assuring profits for both the consumer and the producer during the transaction of electric power trading. Swing options are one type of the contracts these trading schemes offer with respect to the time and amount of energy delivered [1][2][3][4][5]. Such agreements offer flexibility with respect to limitations in the amount of electric energy that can be delivered at a specific time period, production costs and pay-off conditions [6][7][8].…”

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

“…When jump-diffusion processes are considered, a partial-integro differential equation arises. Thus, in [21] the one-factor PIDE is solved by using a finite-difference scheme combined with a dynamic programming technique, while in [27] an implicit-explicit finite difference scheme is proposed. The finite difference method jointly with the approximation of the integral term by means of a recursion formula is also implemented in [5] for the one factor problem under Kou jump-diffusion model.…”

Pricing swing options in electricity markets with two stochastic factors using a partial differential equation approach

“…Jump diffusion processes to describe the evolution of the underlying asset can also be taken into account, thus leading to a partial integro-differential equation. In this setting, a finite difference scheme combined with a dynamic programming technique has been used in Kjaer (2007), and an implicit-explicit finite difference scheme was proposed in Nguyen and Ehrhardt (2012). As indicated in Carmona and Ludkovski (2009), practitioners usually value swing options by simulation techniques; however, the rigorous error analysis associated with many simulation schemes is difficult.…”