A temperature stochastic model for option pricing and its impacts on the electricity market

Electricity use varies with the weather as changes in temperature and humidity affect the demand for space heating and cooling. The residential end-use sector has the largest seasonal variance with significant spikes in demand every summer and winter. Electricity demand is subject to fluctuations on a seasonal basis, across the week, and during the day and can also be influenced by irregular events. The demand for power fluctuates significantly in the electricity market resulting in significant ancillary costs to suppliers. This article describes weather derivatives in electricity markets and applies the risk management hedging technique for the price fluctuation and electricity demand during weather variations. The main objective of this paper is to construct a temperature stochastic model for option pricing and determine its impact on electricity markets. We begin by briefly considering the construction of the temperature stochastic model under a Fractional Brownian motion which is driven by the fractional Itô formula and the fractional Girsanov theorem. We then extend this staging to the weather derivative market and construct a stochastic model for bond weather derivatives and financial derivatives (weather options). Following that, we construct and derive the option-pricing model from the Black–Scholes equation and build a pricing model for weather derivative instruments based on the weather contribution of the electricity market. Finally, we carried out a numerical example that allows us to see that the predicted option pricing values might differ depending on how temperature is forecasted.