Paper: arXiv 2407.21138

Abstract

We present a dynamic hedging scheme for S&P 500 options, where rebalancing decisions are enhanced by integrating information about the implied volatility surface dynamics. The optimal hedging strategy is obtained through a deep policy gradient-type reinforcement learning algorithm. The favorable inclusion of forward-looking information embedded in the volatility surface allows our procedure to outperform several conventional benchmarks such as practitioner and smiled-implied delta hedging procedures, both in simulation and backtesting experiments. The outperformance is more pronounced in the presence of transaction costs.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematics including stochastic calculus, partial differential equations for the JIVR model, and deep reinforcement learning (policy gradient algorithms) for a complex hedging problem. Empirically, it is highly rigorous with backtesting on real S&P 500 option data from OptionMetrics over 25 years, includes transaction costs, and provides reproducible code via GitHub.

Research Flowchart

  flowchart TD
  Goal["Research Goal: Enhance Options Hedging with Volatility Surface Info"]
  --> Input["Data: S&P 500 Options & Volatility Surface Dynamics"]
  
  Input --> Method["Methodology: Deep Policy Gradient RL"]
  Method --> Process["Computational Process: Dynamic Delta Hedging with Vol. Surface Feedback"]
  
  Process --> Outcome["Key Findings: Outperforms Benchmarks & Handles Transaction Costs"]

Cited References (78)

  1. Relationship between deep hedging and delta hedging: leveraging a statistical arbitrage strategy (2023)
  2. Dynamic $L^p$ -hedging in discrete time under cone constraints (2000)
  3. Dynamic hedging of C onditional V alue-at- R isk (2012)
  4. Deep hedging of derivatives using reinforcement learning (2020)
  5. Gamma and vega hedging using deep distributional reinforcement learning (2023)
  6. Deep hedging (2019)
  7. Deep hedging of long-term financial derivatives (2021)
  8. Equal risk pricing of derivatives with deep hedging (2021)
and 70 more
  1. Deep equal risk pricing of financial derivatives with non-translation invariant risk measures (2023)
  2. Options market makers’ hedging and informed trading: Theory and evidence (2015)
  3. Benchmarked risk minimizing hedging strategies for life insurance policies (2019)
  4. Retail Option Trading and Market Quality: Evidence from High-Frequency Data (2023)
  5. Stock price clustering on option expiration dates (2005)
  6. Pre-trade hedging: Evidence from the issuance of retail structured products (2020)
  7. Hedging costs and joint determinants of premiums and spreads in structured financial products (2020)
  8. An out-of-sample analysis of investment guarantees for equity-linked products: Lessons from the financial crisis of the late 2000s (2012)
  9. Options market makers (2023)
  10. A model for the hedging impact of option market makers (2024)
  11. Optimal delta hedging for options (2017)
  12. Approximation capabilities of multilayer feedforward networks (1991)
  13. Volatility and correlation: the perfect hedger and the fox (2004)
  14. Deep Hedging with Options Using the Implied Volatility Surface — → 2504.06208
  15. Delta hedging of derivatives using deep reinforcement learning (2021)
  16. Delta-Gamma–Like Hedging with Transaction Cost under Reinforcement Learning Technique (2022)
  17. Deep learning for discrete-time hedging in incomplete markets (2020)
  18. Probabilistic forecasting of sensory data with generative adversarial networks–for GAN (2019)
  19. Smile-implied hedging with volatility risk (2021)
  20. Option pricing and replication with transactions costs (1985)
  21. Understanding global feature contributions with additive importance measures (2020)
  22. Reinforcement learning: An introduction (2018)
  23. Perfect option hedging for a large trader (1998)
  24. Option replication in discrete time with transaction costs (1992)
  25. The QLBS Q -Learner goes N u QL ear: F itted Q iteration, inverse RL , and option portfolios (2019)
  26. Deep hedging under rough volatility (2021)
  27. Robust deep hedging (2022)
  28. Robust risk-aware option hedging — → 2303.15216
  29. Optimal replication of options with transactions costs and trading restrictions (1993)
  30. Dynamic hedging of single and multi-dimensional options with transaction costs: A generalized utility maximization approach (2008)
  31. Option hedging theory under transaction costs (2009)
  32. On the mean-variance tradeoff in option replication with transactions costs (1996)
  33. Deep hedging: Hedging derivatives under generic market frictions using reinforcement learning (2022)
  34. Deep learning (2016)
  35. Long short-term memory (1997)
  36. Deep equal risk pricing of financial derivatives with multiple hedging instruments (2021) — link
  37. Implied volatility functions: Empirical tests (1998)
  38. Variance-Optimal Hedging in Discrete Time (1995)
  39. Optimal hedging in discrete time (2013) — link
  40. The Pricing of Options and Corporate Liabilities (1973)
  41. Discretely adjusted option hedges (1980) — link
  42. Option Pricing and Replication with Transactions Costs (1985)
  43. Hedging the smirk (2005) — link
  44. Model-free hedge ratios and scale-invariant models (2007) — link
  45. Regime-dependent smile-adjusted delta hedging (2012) — link
  46. Option pricing with transaction costs and a nonlinear Black-Scholes equation (1998)
  47. Optimal hedging when the underlying asset follows a regime-switching M arkov process (2014) — link
  48. Minimizing CV a R in global dynamic hedging with transaction costs (2016) — link
  49. Equal risk pricing and hedging of financial derivatives with convex risk measures (2022) — link
  50. Time consistent dynamic risk measures (2006)
  51. No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging (2021) — link
  52. A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric G aussian Random Walks (2019)
  53. The relationship between put and call option prices (1969)
  54. An empirical analysis of dropout in piecewise linear networks (2013) — link
  55. The K olmogorov- S mirnov, C ram 'e r-von M ises Tests (1957)
  56. Optimal hedging when the underlying asset follows a regime-switching Markov process (2014)
  57. Martingales and stochastic integrals in the theory of continuous trading (1981)
  58. Understanding the difficulty of training deep feedforward neural networks (2010)
  59. Empirical deep hedging (2023)
  60. Deep Reinforcement Learning for Dynamic Stock Option Hedging: A Review (2023)
  61. Quantum deep hedging — → 2303.16585
  62. Deep Hedging with Market Impact — → 2402.13326
  63. Deep reinforcement learning for option replication and hedging (2020)
  64. Deep reinforcement learning for option pricing and hedging under dynamic expectile risk measures (2023) — link
  65. Option hedging for small investors under liquidity costs (2010)
  66. Option pricing and hedging with execution costs and market impact (2017)
  67. The best hedging strategy in the presence of transaction costs (2009)
  68. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993)
  69. Managing smile risk (2002)
  70. Beyond arbitrage: Good-deal asset price bounds in incomplete markets (2000)

4 of 78 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.