Paper: arXiv 2410.11789

Abstract

The volatility fitting is one of the core problems in the equity derivatives business. Through a set of deterministic rules, the degrees of freedom in the implied volatility surface encoding (parametrization, density, diffusion) are defined. Whilst very effective, this approach widespread in the industry is not natively tailored to learn from shifts in market regimes and discover unsuspected optimal behaviors. In this paper, we change the classical paradigm and apply the latest advances in Deep Reinforcement Learning(DRL) to solve the fitting problem. In particular, we show that variants of Deep Deterministic Policy Gradient (DDPG) and Soft Actor Critic (SAC) can achieve at least as good as standard fitting algorithms. Furthermore, we explain why the reinforcement learning framework is appropriate to handle complex objective functions and is natively adapted for online learning.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper utilizes advanced mathematical concepts from reinforcement learning theory and stochastic control, including Markov Decision Processes, value functions, and actor-critic architectures. However, it lacks concrete backtesting results, statistical metrics, or implementation details, relying instead on theoretical assertions and high-level methodology descriptions.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Apply DRL to<br>Volatility Fitting"] --> B["Methodology<br>DDPG & SAC Models"]
  B --> C["Input Data<br>Market Data &<br>Implied Volatility Surface"]
  C --> D["Computational Process<br>Agent-environment Loop<br>with Custom Reward Function"]
  D --> E["Key Findings<br>1. Matches Standard Algorithm Performance<br>2. Handles Complex Objectives<br>3. Enables Online Learning"]

Cited References (35)

  1. Deep Hedging: Continuous Reinforcement Learning for Hedging of General Portfolios across Multiple Risk Aversions (2022) — link
  2. High frequency automated market making algorithms with adverse selection risk control via reinforcement learning (2021) — link
  3. Optimal Trade Execution Based on Deep Deterministic Policy Gradient (2020) — link
  4. An End-to-End Optimal Trade Execution Framework based on Proximal Policy Optimization (2020) — link
  5. Reinforcement Learning in Economics and Finance (2020) — link
  6. Robust Market Making via Adversarial Reinforcement Learning (2020) — link
  7. Deep Hedging of Derivatives Using Reinforcement Learning (2019) — link
  8. Reinforcement Learning for Market Making in a Multi-agent Dealer Market (2019) — link
and 27 more
  1. Modern Perspectives on Reinforcement Learning in Finance (2019) — link
  2. Soft Actor-Critic Algorithms and Applications (2018) — link
  3. Market Making via Reinforcement Learning (2018) — link
  4. Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor (2018) — link
  5. Machine Learning in Finance (2016)
  6. Continuous control with deep reinforcement learning (2015) — link
  7. Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift (2015) — link
  8. Adaptive Market Making via Online Learning (2013)
  9. Generalized Arbitrage-Free SVI Volatility Surfaces (2012) — link
  10. Arbitrage-free SVI volatility surfaces (2012) — link
  11. Implied Volatility Surface: Construction Methodologies and Characteristics (2011) — link
  12. Policy Gradient Methods for Reinforcement Learning with Function Approximation (1999)
  13. Dynamic Programming and Optimal Control. Volume 1 (1996) — link
  14. Technical Note: Q-Learning (1992) — link
  15. Approximation by superpositions of a sigmoidal function (1989) — link
  16. Multilayer feedforward networks are universal approximators (1989) — link
  17. A Stochastic Approximation Method (1951) — link
  18. Sculpting implied volatility surfaces of illiquid assets (2022)
  19. on Advances in (2020)
  20. Deep Learning (2016) — link
  21. Lagrangian Duality for Dummies (2010)
  22. Reinforcement Learning: An Introduction (2005) — link
  23. A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives (2004)
  24. Simple Statistical Gradient-Following Algorithms for Connectionist Reinforcement Learning (2004) — link
  25. Actor-Critic Algorithms (1999)
  26. It takes some action a t i +1 = ∆ ⃗θ t i +1 = θ t i +1 − θ t i on the adjustment of the old parameters ⃗θ t i , and receives some reward r ( s t i +1 , a t i +1 = ∆ ⃗θ t i +1 )
  27. Advanced Volatility Fitting

0 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.