Pricing Carbon Allowance Options on Futures: Insights from High-Frequency Data

Paper: arXiv 2501.17490

Authors: Simone Serafini, Giacomo Bormetti

Abstract

Leveraging a unique dataset of carbon futures option prices traded on the ICE market from December 2015 until December 2020, we present the results from an unprecedented calibration exercise. Within a multifactor stochastic volatility framework with jumps, we employ a three-dimensional pricing kernel compensating for equity and variance components’ risk to derive an analytically tractable and numerically practical approach to pricing. To the best of our knowledge, we are the first to provide an estimate of the equity and variance risk premia for the carbon futures option market. We gain insights into daily option and futures dynamics by exploiting the information from tick-by-tick futures trade data. Decomposing the realized measure of futures volatility into continuous and jump components, we employ them as auxiliary variables for estimating futures dynamics via indirect inference. Our approach provides a realistic description of carbon futures price, volatility, and jump dynamics and an insightful understanding of the carbon option market.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a strong combination of sophisticated mathematical modeling (a multi-factor stochastic volatility model with jumps and a 3D pricing kernel) with high empirical rigor using tick-by-tick carbon futures data. It achieves a notable milestone as one of the first studies to estimate equity and variance risk premia specifically for the carbon allowance options market.

Research Flowchart

  flowchart TD
    A[Research Goal: Price Carbon Allowance Options & Estimate Risk Premia] --> B[Data Inputs: ICE Tick-by-Tick Futures & Options Data 2015-2020]
    B --> C[Methodology Part 1: Decompose Futures Volatility into Continuous & Jump Components]
    C --> D[Methodology Part 2: Indirect Inference Estimation of Futures Dynamics]
    D --> E[Methodology Part 3: Multifactor Stochastic Volatility Model with 3D Pricing Kernel]
    E --> F[Key Findings: Realistic Carbon Futures/Jump Dynamics & First Estimates of Carbon Equity/Variance Risk Premia]