Paper: arXiv 2402.17941

Abstract

In this paper, we present an artificial neural network framework for portfolio compression of a large portfolio of European options with varying maturities (target portfolio) by a significantly smaller portfolio of European options with shorter or same maturity (compressed portfolio), which also represents a self-replicating static hedge portfolio of the target portfolio. For the proposed machine learning architecture, which is consummately interpretable by choice of design, we also define the algorithm to learn model parameters by providing a parameter initialisation technique and leveraging the optimisation methodology proposed in Lokeshwar and Jain (2024), which was initially introduced to price Bermudan options. We demonstrate the convergence of errors and the iterative evolution of neural network parameters over the course of optimization process, using selected target portfolio samples for illustration. We demonstrate through numerical examples that the Exposure distributions and Exposure profiles (Expected Exposure and Potential Future Exposure) of the target portfolio and compressed portfolio align closely across future risk horizons under risk-neutral and real-world scenarios. Additionally, we benchmark the target portfolio’s Financial Greeks (Delta, Gamma, and Vega) against the compressed portfolio at future time horizons across different market scenarios generated by Monte-Carlo simulations. Finally, we compare the regulatory capital requirement under the standardised approach for counterparty credit risk of the target portfolio against the compressed portfolio and highlight that the capital requirement for the compact portfolio substantially reduces.

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 uses advanced neural network architectures, optimization theory, and risk-neutral pricing mathematics, while also presenting detailed numerical examples, Monte-Carlo simulations, and specific metrics (exposure profiles, Greeks, capital requirements) demonstrating a backtest-ready implementation.

Research Flowchart

  flowchart TD
  A["Research Goal: Develop interpretable ANN<br>for portfolio compression & static hedging"] --> B["Input: Large Target Portfolio<br>European Options"]
  B --> C["Key Methodology: ANN Architecture<br>with Parameter Initialization & Optimization"]
  C --> D["Computation: Monte-Carlo Simulations<br>Iterative Parameter Learning"]
  D --> E["Outcome 1: Aligned Risk Exposures<br>EE & PFE across Risk Horizons"]
  D --> F["Outcome 2: Consistent Greeks<br>Delta, Gamma, Vega Benchmark"]
  D --> G["Outcome 3: Reduced Capital Requirements<br>Standardised Approach for CCR"]

Cited References (136)

  1. Explainable neural network for pricing and universal static hedging of contingent claims (2022)
  2. Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions (2009)
  3. Valuing American options by simulation: a simple least-squares approach (2001)
  4. The pricing of options and corporate liabilities (1973)
  5. Neural networks for pattern recognition (1995)
  6. Adam: A method for stochastic optimization (2014) — link
  7. Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods (2012)
  8. Valuation of the early-exercise price for options using simulations and nonparametric regression (1996)
and 128 more
  1. Regression methods for pricing complex American-style options (2001)
  2. An analysis of a least squares regression method for American option pricing (2002)
  3. Number of paths versus number of basis functions in American option pricing (2004)
  4. A fast and accurate FFT-based method for pricing early-exercise options under L 'e vy processes (2008)
  5. Pricing of High-Dimensional American Options by Neural Networks (2010)
  6. Solving high-dimensional optimal stopping problems using deep learning (2021)
  7. Neural network regression for Bermudan option pricing (2021)
  8. Deep neural network framework based on backward stochastic differential equations for pricing and hedging american options in high dimensions (2021)
  9. Deep xVA Solver: A Neural Network–Based Counterparty Credit Risk Management Framework (2023)
  10. Efficient computation of exposure profiles for counterparty credit risk (2014)
  11. The stochastic grid bundling method: Efficient pricing of Bermudan options and their Greeks (2015)
  12. Counterparty credit exposures for interest rate derivatives using the stochastic grid bundling method (2016)
  13. A novel pricing method for European options based on Fourier-cosine series expansions (2009)
  14. Mathematical modeling and computation in finance: with exercises and Python and MATLAB computer codes (2019)
  15. Deep hedging (2019)
  16. Machine learning for quantitative finance: fast derivative pricing, hedging and fitting (2018)
  17. Pricing options and computing implied volatilities using neural networks (2019)
  18. A neural network-based framework for financial model calibration (2019)
  19. Empirical asset pricing via machine learning (2020)
  20. Static hedging of standard options (2014)
  21. A test for superior predictive ability (2005)
  22. The difference between LSMC and replicating portfolio in insurance liability modeling (2016)
  23. Delta-hedged gains and the negative market volatility risk premium (2003)
  24. Options: A monte carlo approach (1977)
  25. Simulation for American options: Regression now or regression later? (2004)
  26. Pricing American options by simulation using a stochastic mesh with optimized weights (2000)
  27. A Sotchastic Mesh Method for Pricing High-Dimensional American Options (1997)
  28. Pricing high-dimensional American options by kernel ridge regression (2020)
  29. Fast convergence of regress-later estimates in least squares Monte Carlo (2013) — link
  30. A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options (2021)
  31. Deep optimal stopping (2019)
  32. Dynamic programming (1966)
  33. Pricing and hedging American-style options with deep learning (2020)
  34. A reality check for data snooping (2000)
  35. Comparing predictive accuracy (2002)
  36. Asymptotic inference about predictive ability (1996)
  37. A forecast comparison of volatility models: does anything beat a GARCH (1, 1)? (2005)
  38. Regression-based tests of predictive ability (1998)
  39. Robust hedging of barrier options (2001)
  40. The feedback effect of hedging in illiquid markets (2000)
  41. An improved method for pricing and hedging long dated American options (2016)
  42. Robust hedging of the lookback option (1998)
  43. Calibration and hedging under jump diffusion (2006)
  44. Dynamic hedging in a volatile market (2003)
  45. Reconstructing the unknown local volatility function (2001)
  46. Dynamic hedging under jump diffusion with transaction costs (2009)
  47. Prices of state-contingent claims implicit in option prices (1978)
  48. Spanning and completeness in markets with contingent claims (1987)
  49. Spanning and completeness with options (1988)
  50. Optimal positioning in derivative securities (2001)
  51. Static hedging of exotic options (1998)
  52. A new scheme for static hedging of European derivatives under stochastic volatility models (2009)
  53. Efficient Static Replication of European Options for Exponential Levy Models (Revised in January 2008, Published in" Journal of Futures Markets", Vol. 29-1, 1-15, 2009.) (2007)
  54. Static hedging under time-homogeneous diffusions (2011)
  55. Simple robust hedging with nearby contracts (2016)
  56. Optimal static quadratic hedging (2016)
  57. A functional analysis approach to the static replication of European options (2021)
  58. Static replication of European standard dispersion options (2022)
  59. A Macroprudential View on Portfolio Rebalancing and Compression (2021)
  60. A Note on Portfolio Compression for Plain Vanilla Interest Rate Swaps (2014)
  61. Compressing over-the-counter markets (2021)
  62. BASEL Framework CRE52, Standardised Approach to Counterpart Credit Risk (2020)
  63. The practice of portfolio replication. A practical overview of forward and inverse problems (1999)
  64. Distress and default contagion in financial networks (2020)
  65. Optimal network compression (2022)
  66. Optimal portfolio selection and compression in an incomplete market (2001)
  67. Optimising the multilateral netting of fungible OTC derivatives (2017)
  68. Llama: Open and efficient foundation language models (2023) — link
  69. A logical calculus of the ideas immanent in nervous activity (1943)
  70. The perceptron: a probabilistic model for information storage and organization in the brain. (1958)
  71. Adaptive switching circuits (No. TR-1553-1) (1960)
  72. Cognitron: A self-organizing multilayered neural network (1975)
  73. Self-organized formation of topologically correct feature maps (1982)
  74. Beyond regression: New tools for prediction and analysis in the behavioral sciences (1974)
  75. Learning internal representations by error propagation (1985)
  76. R egress- L ater Monte Carlo for optimal control of Markov processes (2017) — link
  77. Rolling Adjoints: fast G reeks along M onte C arlo scenarios for early-exercise options (2019)
  78. Efficient computation of exposure profiles on real-world and risk-neutral scenarios for B ermudan swaptions (2016)
  79. KVA , M ind Your P ’s and Q ’s! (2019)
  80. Pricing and hedging guaranteed annuity options via static option replication (2003)
  81. Static hedging of multivariate derivatives by simulation (2005)
  82. Deep Smoothing of the Implied Volatility Surface (2019) — link
  83. On deep calibration of (rough) stochastic volatility models (2019) — link
  84. Pricing A merican options: a duality approach (2004)
  85. Monte C arlo valuation of A merican options (2002)
  86. Efficient hierarchical approximation of high-dimensional option pricing problems (2007)
  87. Comonotonic Monte Carlo Simulation and Its Applications in Option Pricing and Quantification of Risk (2016)
  88. Improved lower and upper bound algorithms for pricing A merican options by simulation (2008)
  89. Primal-dual simulation algorithm for pricing multidimensional A merican options (2004)
  90. GPU acceleration of the stochastic grid bundling method for early-exercise options (2015)
  91. Multilayer feedforward networks are universal approximators (1989)
  92. Multilayer feedforward networks with a nonpolynomial activation function can approximate any function (1993)
  93. Connecting discrete and continuous path-dependent options (1999)
  94. A continuity correction for discrete barrier options (1997)
  95. Report on post trade risk reduction services with regards to the clearing obligation (2020)
  96. Risk management: History, definition, and critique (2013)
  97. The credit default swap market: what a difference a decade makes (2018)
  98. The evolution of OTC interest rate derivatives markets (2019)
  99. Outstanding OTC derivatives positions dwindle as compression gains further traction (2015)
  100. When does portfolio compression reduce systemic risk? (2022)
  101. Static options replication (1995)
  102. Dynamic portfolio replication using stochastic programming (2002)
  103. Machine learning in banking risk management: A literature review (2019)
  104. A semi-static replication approach to efficient hedging and pricing of callable IR derivatives (2022) — link
  105. Implied volatility surface: Construction methodologies and characteristics (2011) — link
  106. Stochastic differential equations (2003)
  107. Stochastic calculus for finance II: Continuous-time models (2004)
  108. Regression shrinkage and selection via the lasso (1996)
  109. An algorithm with guaranteed convergence for finding a zero of a function (1971)
  110. The stationary bootstrap (1994)
  111. Automatic block-length selection for the dependent bootstrap (2004)
  112. Robust deep hedging (2022)
  113. Put-call symmetry: Extensions and applications (2009)
  114. Consistency of the stationary bootstrap under weak moment conditions (2003)
  115. OTC derivatives statistics at end-June 2023 (2023)
  116. Basel Committee on Banking Supervision (2019)
  117. Machine learning for financial risk management: a survey (2020)
  118. Explainable ai: A review of machine learning interpretability methods (2020)
  119. Peeking inside the black-box: a survey on explainable artificial intelligence (XAI) (2018)
  120. Towards a rigorous science of interpretable machine learning (2017) — link
  121. Explanation in artificial intelligence: Insights from the social sciences (2019)
  122. Interpretable machine learning: Fundamental principles and 10 grand challenges (2022)
  123. Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead (2019)
  124. " How do I fool you?" Manipulating User Trust via Misleading Black Box Explanations (2020)
  125. The dangers of post-hoc interpretability: Unjustified counterfactual explanations (2019) — link
  126. Ai in finance: challenges, techniques, and opportunities (2022)
  127. Optimizing Neural Networks for Bermudan Option Pricing: Convergence Acceleration, Future Exposure Evaluation and Interpolation in Counterparty Credit Risk — → 2402.15936
  128. Data-driven Approach for Static Hedging of Exchange Traded Options — → 2302.00728

2 of 136 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.