Paper: arXiv 2212.07972
Authors: Orcan Ogetbil, Bernhard Hientzsch
Abstract
We propose a non-parametric extension with leverage functions to the Andersen commodity curve model. We calibrate this model to market data for WTI and NG including option skew at the standard maturities. While the model can be calibrated by an analytical formula for the deterministic rate case, the stochastic rate case demands estimation of an expectation for which we employ Monte Carlo simulation. We find that the market smile is captured for the deterministic rate case; and with relatively low number of paths, for the stochastic rate case. Since there is typically at most one standard maturity with liquid volatility data for each futures contract, there is flexibility on the shape of nonstandard maturity implied volatility and how the total implied variance accumulates. We equip the model with different total implied variance accumulators to demonstrate that flexibility.
Complexity vs Empirical Score
- Math Complexity: 6.5/10
- Empirical Rigor: 5.5/10
- Quadrant: Holy Grail — high math complexity, high empirical rigor
Why this score: The paper presents a solid extension to the Andersen commodity curve model using local/leverage volatility functions and stochastic rates. It offers strong mathematical formulation for option skew calibration, though empirical validation is limited to standard WTI and NG market data without extensive out-of-sample backtesting.
Research Flowchart
flowchart TD
A[Research Goal: Capture Commodity Option Skew & Maturity Effects] --> B[Data Inputs: WTI & NG Market Data + Option Skew]
B --> C[Methodology: Extend Andersen Model with Non-Parametric Leverage Functions]
C --> D{Interest Rate Case?}
D -- Deterministic Rates --> E[Analytical Formula Calibration]
D -- Stochastic Rates --> F[Monte Carlo Simulation Estimation]
E & F --> G[Apply Flexible Total Implied Variance Accumulators]
G --> H[Outcomes: Successfully Captured Market Smile & Controlled Nonstandard Maturity Volatility]