Paper: arXiv 2603.26514

Authors: Roberto Daluiso, Héctor Folgar-Cameán, Andrea Pallavicini, Carlos Vázquez

Abstract

In this paper, we develop a general rough volatility model for commodities that provides an automatic calibration of the initial term structure of the futures prices and an appropriate treatment of the Samuelson effect. After the theoretical analysis of this general model, we focus on the rBergomi and rHeston models and their calibration to market data of vanilla futures options on WTI Crude Oil. Finally, numerical results illustrate the performance of the proposed rough volatility models for commodities pricing.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated framework extending rough volatility (rBergomi and rHeston) to commodity futures while accounting for the Samuelson effect. The empirical work effectively demonstrates calibration to WTI crude oil options data, providing a strong blend of advanced mathematical finance and practical calibration techniques.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Develop Rough Volatility Model for Commodities<br><i>(Addressing Samuelson Effect & Term Structure)</i>"] --> B["Data Inputs:<br>WTI Crude Oil Vanilla Futures Options"]
    
    B --> C["Model Specification:<br>Formulate General Model, rBergomi & rHeston"]
    
    C --> D["Calibration & Computation:<br>Automatic Calibration to Initial Futures Term Structure"]
    
    D --> E["Key Outcomes:<br>Accurate Commodity Pricing & Robust Samuelson Effect Treatment"]

Cited References (28)

  1. Forecasting volatility in commodity markets with long-memory models (2022) — link
  2. Hybrid scheme for B rownian semistationary processes (2017) — link
  3. Deep calibration with random grids — → 2306.11061
  4. Stochastic Volatility Modeling (2015)
  5. Is there a term structure of futures volatilities? R eevaluating the S amuelson hypothesis (1995) — link
  6. The pricing of options and corporate liabilities (1973) — link
  7. Smile dynamics and rough volatility (2024)
  8. Consistent variance curve models (2006) — link
and 20 more
  1. Local volatility of volatility for the VIX market (2013) — link
  2. Perfect hedging in rough H eston models (2018) — link
  3. Short-time at-the-money skew and rough fractional volatility (2017) — link
  4. On the martingale property in the rough B ergomi model (2019) — link
  5. Efficient simulation of affine forward variance models (2022)
  6. Volatility is rough (2014) — link
  7. Competing hypotheses on the S amuelson effect in futures markets (2023) — link
  8. Stochastic Differential Equations and Diffusion Processes (1989)
  9. Wiener spirals and some other interesting curves in H ilbert space (1940)
  10. Fractional B rownian motions, fractional noises and applications (1968) — link
  11. Elementary Stochastic Calculus with Finance in View (2004)
  12. Stochastic Calculus for Fractional B rownian Motion and Related Processes (2008)
  13. From constant to rough: A survey of continuous volatility modeling (2023) — link
  14. Smile modelling in commodity markets (2020) — link
  15. Arbitrage with fractional B rownian motion (1997) — link
  16. Proof that properly anticipated prices fluctuate randomly (1965)
  17. Explicit option pricing formula for mean-reverting asset in energy market (2008)
  18. Rough volatility of B itcoin (2020) — link
  19. Pricing under rough volatility (2016) — link
  20. Multifactor Approximation of Rough Volatility Models (2019) — link

1 of 28 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.