Abstract
In this paper, we study the valuation of swing options on electricity in a model where the underlying spot price is set to be the product of a deterministic seasonal pattern and Ornstein-Uhlenbeck process with Markov-modulated parameters. Under this setting, the difficulties of pricing swing options come from the various constraints embedded in contracts, e.g., the total number of rights constraint, the refraction time constraint, the local volume constraint, and the global volume constraint. Here we propose a framework for the valuation of the swing option on the condition that all the above constraints are nontrivial. To be specific, we formulate the pricing problem as an optimal stochastic control problem, which can be solved by the trinomial forest dynamic programming approach. Besides, empirical analysis is carried out on the model. We collect historical data in Nord Pool electricity market, extract the seasonal pattern, calibrate the Ornstein-Uhlenbeck process parameters in each regime, and also get market price of risk. Finally, on the basis of calibration results, a specific numerical example concerning all typical constraints is presented to demonstrate the valuation procedure.
Highlights
In the long run, energy liberalisation in electricity markets improves economic benefits, since that it overcomes the overcapacity problem in regulated markets and improves efficiency in the operation of networks and transport services
We study the valuation of swing options on electricity in a model where the underlying spot price is set to be the product of a deterministic seasonal pattern and Ornstein-Uhlenbeck process with Markov-modulated parameters
Under the settings that the underlying asset follows a seasonal mean-reverting regime-switching model with n regimes and that some typical constraints are nontrivial, we have proposed a trinomial forest framework for the valuation of the swing option, which is a multiple-layer tree extension of the traditional trinomial tree approach
Summary
Energy liberalisation in electricity markets improves economic benefits, since that it overcomes the overcapacity problem in regulated markets and improves efficiency in the operation of networks and transport services (see [1] for more detail). The valuation problem can be formulated as an optimal stochastic control problem subject to constraints Facing this problem, many researchers employed the dynamic programming method, which lead to the Bellman’s equation for the value function. As for the constraints of option, besides usual ones, we take refraction time constraint and a penalty function of more general form into consideration based on [22] Under these settings, we formulate the pricing of swings as an optimal stochastic control problem subject to several constraints, including the refraction time, the local volume, and the global volume. Based on the daily average data in Nord Pool, we calibrate the model with two regimes and construct a concrete example concerning all nontrivial constraints and a penalty function of general form.
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