The Market Price of Jump Risk for Delivery Periods: Pricing of Electricity Swaps with Geometric Averaging

Paper: arXiv 2303.12527

Authors: Annika Kemper, Maren Diane Schmeck

Abstract

In this paper, we extend the market price of risk for delivery periods (MPDP) of electricity swap contracts by introducing a dimension for jump risk. As introduced by Kemper et al. (2022), the MPDP arises through the use of geometric averaging while pricing electricity swaps in a geometric framework. We adjust the work by Kemper et al. (2022) in two directions: First, we examine a Merton type model taking jumps into account. Second, we transfer the model to the physical measure by implementing mean-reverting behavior. We compare swap prices resulting from the classical arithmetic (approximated) average to the geometric weighted average. Under the physical measure, we discover a decomposition of the swap’s market price of risk into the classical one and the MPDP.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical contribution by extending electricity swap pricing models to incorporate jump risks under geometric averaging and physical measures. However, it relies predominantly on mathematical derivations with little to no empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Extend MPDP for Electricity Swaps by Incorporating Jump Risk"] --> B["Inputs: Spot Price Dynamics with Jumps & Mean-Reversion"]
    B --> C["Model Extension: Merton Jump-Diffusion under Physical Measure"]
    C --> D["Pricing Framework: Geometric Averaging vs. Arithmetic Approximation"]
    D --> E["Findings: MPDP Decomposition into Classical Risk & Delivery Period Risk"]