Valuation of spark-spread options with mean reversion and stochastic volatility
Résumé
In the electricity market, spark-spread options are increasingly used for hedging purposes and for valuing natural gas power plants. A spark-spread option gives the buyer the right but not the obligation to buy the price difference between electricity and natural gas adjusted for power plant efficiency. Pricing these options requires stochastic process models for the electricity price and the gas price, and the correlation between the two. Here we use mean-reverting models (together with a seasonal trend) to model both electricity and gas. Two variants are considered for electricity: one with constant volatility and one with stochastic volatility. The latter is compatible with the short bursts of high volatility observed in many deregulated markets. Rather than fitting all the parameters simultaneously, we use a 3-step procedure in which the seasonality is estimated first, then the speed of mean reversion, then the other parameters. An innovative feature is that the variogram, a tool from spatial statistics, is used to fit the mean-reversion speed. We investigate the impact of volatility on the price of the spark-spread option, using data from continental Europe as an example. The results show that the model with stochastic volatility gives significantly higher spark-spread values. Moreover, the spark-spread option prices are very sensitive to the correlation factor between electricity and natural gas, especially if the electricity price follows a simple mean-reverting process with constant volatility.