A pricing measure to explain the risk premium in power markets

TL;DR

This paper introduces a new pricing measure for power markets that extends the Esscher transform, enabling more flexible modeling of risk premiums and spot price dynamics, including stochastic sign changes and stationarity.

Contribution

It proposes an extended change of measure that allows for stochastic risk premiums with non-constant sign and stationary spot dynamics in power market models.

Findings

Enables stochastic risk premiums with stochastic sign changes.

Allows for stationary spot price dynamics with fluctuating forward prices.

Provides a flexible framework for modeling risk profiles across maturities.

Abstract

In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other factor is an OU process driven by a pure jump L\'evy process and models the characteristic spikes observed in such markets. When it comes to pricing, a popular choice of pricing measure is given by the Esscher transform that preserves the probabilistic structure of the driving L\'evy processes, while changing the levels of mean reversion. Using this choice one can generate stochastic risk premiums (in geometric spot models) but with (deterministically) changing sign. In this paper we introduce a pricing change of measure, which is an extension of the Esscher transform. With this new change of measure we also can slow down the speed of mean reversion and generate stochastic risk premiums with stochastic non constant sign, even in arithmetic spot models. In particular, we can generate risk profiles with positive values in the short end of the forward curve and negative values in the long end. Finally, our pricing measure allows us to have a stationary spot dynamics while still having randomly fluctuating forward prices for contracts far from maturity.