Paper: arXiv 2409.19385

Abstract

PDSim is an R package that enables users to simulate commodity futures prices using the polynomial diffusion model introduced in Filipovic & Larsson (2016) through both a Shiny web application and R scripts. For user-supplied data, a standalone R routine has been developed to provide joint estimation of state variables and model parameters via the Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF). With its user-friendly interface, PDSim makes the features of simulations and estimations accessible. To date, it is the only package specifically designed for the simulation and estimation of the polynomial diffusion model. The Schwartz-Smith two-factor model (Schwartz & Smith, 2000) is also available within this package for both simulation and calibration. The package is validated through several tests, including replication of the results in Schwartz & Smith (2000), unit testing of the coverage rate, and verification of the outputs of the main functions.

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 contains dense mathematical derivations involving polynomial diffusions, SDEs, and generator theory (Theorem 1), but the software implementation focuses on simulation and estimation tools with limited backtesting on real data, placing it in the ‘Lab Rats’ quadrant.

Research Flowchart

  flowchart TD
  A["Research Goal: Develop R Package for<br>Simulating/Estimating Polynomial Diffusion Models"] --> B["Methodology: Model Implementation<br>Polynomial Diffusion & Schwartz-Smith"]
  B --> C["Methodology: Estimation Technique<br>Extended/Unscented Kalman Filters"]
  C --> D["Methodology: Validation & Testing<br>Replication & Unit Testing"]
  D --> E["Data Input: User-Supplied<br>Commodity Futures Data"]
  D --> F["Computational Process: Shiny App<br>GUI & R Package Backend"]
  E --> F
  F --> G["Key Outcomes: PDSim Package<br>Simulation & Estimation Tools"]
  G --> H["Final Outcome: Validated &<br>User-Friendly R Package"]

Cited References (25)

  1. Multi-Factor Polynomial Diffusion Models and Inter-Temporal Futures Dynamics — → 2409.19386
  2. Polynomial diffusions and applications in finance (2016)
  3. NFCP : N-Factor Commodity Pricing Through Term Structure Estimation (2021)
  4. Forecasting, structural time series models and the Kalman filter (1990)
  5. New extension of the Kalman filter to nonlinear systems (1997)
  6. Unscented filtering and nonlinear estimation (2004)
  7. A multifactor polynomial framework for long-term electricity forwards with delivery period (2020)
  8. Short-term variations and long-term dynamics in commodity prices (2000)
and 17 more
  1. The unscented Kalman filter for nonlinear estimation (2000)
  2. Which risk factors drive oil futures price curves? (2020)
  3. Stochastic convenience yield implied from commodity futures and interest rates (2005)
  4. Commodity price forecasts, futures prices, and pricing models (2019)
  5. An N -factor Gaussian model of oil futures prices (2006)
  6. Energy futures prices: term structure models with Kalman filter estimation (2002)
  7. Calibration and filtering for multi factor commodity models with seasonality: incorporating panel data from futures contracts (2013)
  8. Modeling seasonality in agricultural commodity futures (2002)
  9. Stochastic convenience yield and the pricing of oil contingent claims (1990)
  10. A two-factor model for the electricity forward market (2009)
  11. Parameter estimation for a bidimensional partially observed Ornstein–Uhlenbeck process with biological application (2010)
  12. A limited memory algorithm for bound constrained optimization (1995)
  13. The negative pricing of the May 2020 WTI contract (2023)
  14. Jumps in commodity markets (2019)
  15. Jump activity analysis for affine jump-diffusion models: Evidence from the commodity market (2019)
  16. Forecasting commodity prices: GARCH , jumps, and mean reversion (2008)
  17. Polynomial jump-diffusion models (2020)

1 of 25 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.