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Valuation of Spark-Spread Option Written on Electricity and Gas Forward Contracts Under Two-Factor Models with Non-Gaussian Lévy Processes

Author

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  • Farshid Mehrdoust

    (University of Guilan)

  • Idin Noorani

    (University of Guilan)

Abstract

In energy markets, especially electricity and gas, one experience rather large and dramatic spikes in spot prices, but they are quickly reverting back. Hence it is appropriate to take into account the factors for the spike behavior observed in the spot price series, while other factors induce price evolution when the market is stable. To illustrate this issue, we analyze the dynamics of spikes and seasonality through a normal probability test for returns of spot prices. We propose two-factor model separately for gas and electricity markets, such that in both market model the logarithmic spot price is a stationary Ornstein-Uhlenbeck process and the long-term variations are a drifted Brownian motion. We derive the forward price and its dynamic under proposed model and prove the uniqueness of solution of the stochastic differential equation related to forward price. Then we price the spark-spread option written on electricity and gas forward contracts. In the following, we derive the spark-spread option price under a hybrid geometric Brownian motion and prove that it converges to the sparks-spread option price under the proposed two-factor model. Since the market model is incomplete, we apply the quadratic hedging strategy which minimizes the hedging error. We also investigate the convergence of this strategy through the spark-spread option under the hybrid geometric Brownian motion. Numerical results confirm the achievement of all these convergences. In order to estimate the model parameters, we consider the Lévy processes as the independent normal inverse Gaussian processes and independent compound Poisson processes which have the jump size with the exponential distribution.

Suggested Citation

  • Farshid Mehrdoust & Idin Noorani, 2023. "Valuation of Spark-Spread Option Written on Electricity and Gas Forward Contracts Under Two-Factor Models with Non-Gaussian Lévy Processes," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 807-853, February.
    • Handle: RePEc:kap:compec:v:61:y:2023:i:2:d:10.1007_s10614-021-10232-4
    DOI: 10.1007/s10614-021-10232-4
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    References listed on IDEAS

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    1. Mehrdoust, Farshid & Noorani, Idin & Kanniainen, Juho, 2024. "Valuation of option price in commodity markets described by a Markov-switching model: A case study of WTI crude oil market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 228-269.

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