Paper: arXiv 2512.19821

Authors: Fabien Le Floc’h

Abstract

Based on the existing literature, this article presents the different ways of choosing the parameters of stochastic volatility models in general, in the context of pricing financial derivative contracts. This includes the use of stochastic volatility inside stochastic local volatility models.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents advanced stochastic differential equations (SDEs) and derivations for multiple SV models, indicating high mathematical density, but it is a review article with no datasets, backtests, or implementation details for practical trading.

Research Flowchart

  flowchart TD
  RQ["Research Question<br>How to choose SV parameters?"] --> Input["Data: Derivative Pricing Context<br>SV & SVSLV Models"]
  Input --> Method["Methodology: Literature Review"]
  Method --> Comp["Computation: Parameter Estimation<br>via ML, GMM, MCMC"]
  Comp --> Out["Findings: Parameter Selection<br>Guidelines & Outcomes"]

Cited References (31)

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  2. Stochastic volatility models and products (2004)
  3. Consistent variance curve models (2006)
  4. Towards a theory of volatility trading (2001)
  5. Foreign exchange option pricing: a practitioner’s guide (2011)
  6. The small-time smile and term structure of implied volatility under the Heston model (2012)
  7. Managing smile risk (2002)
  8. Implied volatility formulas for Heston models (2018)
and 23 more
  1. Applied Quantitative Finance for Equity Derivatives (2025)
  2. Calibrating Heston to Variance Swaps - a bad idea? (2025)
  3. Equity hybrid derivatives (2007)
  4. Manufacturing and managing customer-driven derivatives (2016)
  5. Fourier Integration and Stochastic Volatility Calibration (2014)
  6. The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well (2009)
  7. Stochastic volatility with an Ornstein–Uhlenbeck process: an extension (1999)
  8. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  9. The smile calibration problem solved (2011)
  10. Explicit SABR Calibration Through Simple Expansions (2014) — link
  11. Interest Rate Modeling–Volume I (2010)
  12. Smile pricing explained (2014)
  13. Stochastic local volatility (2010)
  14. Option pricing when the variance changes randomly: Theory, estimation, and an application (1987)
  15. Calibrating and pricing with embedded local volatility models (2007)
  16. Stochastic Volatility Models: Foreign Exchange (2010)
  17. FX smile in the Heston model (2011)
  18. Mixed Local Volatility Boosts Distribution of Exotics (2020)
  19. The Tremor Stochastic-Local-Volatility Model: Independent Validation by Math-Finance (2011)
  20. Affine concatenation (2009)
  21. Heston model: the variance swap calibration (2014)
  22. Heston’s stochastic volatility model: Implementation, calibration and some extensions (2004)
  23. Applications of Fourier transform to smile modeling: Theory and implementation (2009)

0 of 31 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.