A Pricing Measure for Stochastic Risk Premia in Power Markets

Summary

The paper develops a pricing measure for electricity markets with mean-reverting spot prices and sharp price spikes. Its two-factor model represents smaller movements with a Brownian-driven Ornstein–Uhlenbeck process and spikes with a second mean-reverting process driven by a pure-jump Lévy process. The authors contrast their approach with the Esscher transform, which preserves the driving processes’ probabilistic structure but can produce stochastic risk premia whose sign changes deterministically.

Their extension to the Esscher transform can slow mean reversion and generate stochastic risk premia with a sign that varies randomly, including in arithmetic spot models. This permits risk profiles with positive short-maturity and negative long-maturity forward premia. The measure can also retain stationary spot dynamics while allowing distant forward prices to fluctuate randomly. The document describes modeling and pricing properties, but supplies no empirical calibration, performance comparison, or evidence that a particular measure best fits observed market prices.

Key ideas

• Electricity spot prices are modeled with two mean-reverting factors for ordinary variation and price spikes.
• The spike component is driven by a pure-jump Lévy process.
• An extension of the Esscher transform changes mean-reversion behavior and allows stochastic risk-premium signs.
• The model can represent positive premia at the short end and negative premia at the long end of the forward curve.
• Stationary spot dynamics can coexist with fluctuating prices for distant forward contracts.

Tags

# A pricing measure to explain the risk premium in power markets


# A pricing measure to explain the risk premium in power markets









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 Lévy 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 Lévy 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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.