Paper: arXiv 2411.02375

Abstract

Calibrating the time-dependent Implied Volatility Surface (IVS) using sparse market data is an essential challenge in computational finance, particularly for real-time applications. This task requires not only fitting market data but also satisfying a specified partial differential equation (PDE) and no-arbitrage conditions modelled by differential inequalities. This paper proposes a novel Physics-Informed Neural Networks (PINNs) approach called Whack-a-mole Online Learning (WamOL) to address this multi-objective optimisation problem. WamOL integrates self-adaptive and auto-balancing processes for each loss term, efficiently reweighting objective functions to ensure smooth surface fitting while adhering to PDE and no-arbitrage constraints and updating for intraday predictions. In our experiments, WamOL demonstrates superior performance in calibrating intraday IVS from uneven and sparse market data, effectively capturing the dynamic evolution of option prices and associated risk profiles. This approach offers an efficient solution for intraday IVS calibration, extending PINNs applications and providing a method for real-time financial modelling.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents advanced mathematical formalisms including PDEs, differential inequalities, and specialized loss functions (PINNs/DCPINNs) for a complex calibration problem. It demonstrates empirical rigor through backtesting on real market data and evaluating computational efficiency, though the absence of publicly available code or datasets slightly limits full replicability.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Intraday IVS Calibration<br>from Sparse Market Data"] --> B["Methodology: WamOL Framework"]
  
  B --> C{"Data & Inputs:<br>Market Data +<br>PDE/No-Arbitrage Constraints"}
  C --> D["Computational Process:<br>Self-Adaptive & Auto-Balancing<br>Multi-Objective Loss Optimization"]
  D --> E["Key Findings:<br>Superior IVS Calibration<br>Dynamic Risk Profiling<br>Real-time Applicability"]

Cited References (44)

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  5. No-Arbitrage Deep Calibration for Volatility Smile and Skewness — → 2310.16703
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and 36 more
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2 of 44 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.