Whack-a-mole Online Learning: Physics-Informed Neural Network for Intraday Implied Volatility Surface (2411.02375v1)
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.
- Deep smoothing of the implied volatility surface. Advances in Neural Information Processing Systems 33 (2020), 11552–11563.
- Yacine Aıt-Sahalia and Jefferson Duarte. 2003. Nonparametric option pricing under shape restrictions. Journal of Econometrics 116, 1-2 (2003), 9–47.
- Jesper Andreasen and Brian Huge. 2011. Volatility interpolation. Risk 24, 3 (2011), 76.
- The application of improved physics-informed neural network (IPINN) method in finance. Nonlinear Dynamics 107, 4 (2022), 3655–3667.
- Philippe Balland. 2002. Deterministicimplied volatility models. Quantitative Finance 2, 1 (2002), 31.
- Variational autoencoders: A hands-off approach to volatility. The Journal of Financial Data Science 4, 2 (2022), 125–138.
- Fischer Black. 1976. The pricing of commodity contracts. Journal of financial economics 3, 1-2 (1976), 167–179.
- Fischer Black and Myron Scholes. 1973. The pricing of options and corporate liabilities. Journal of political economy 81, 3 (1973), 637–654.
- JAX: composable transformations of Python+NumPy programs. http://github.com/google/jax
- Option valuation under no-arbitrage constraints with neural networks. European Journal of Operational Research 293, 1 (2021), 361–374.
- Peter Carr and Dilip B Madan. 2005. A note on sufficient conditions for no arbitrage. Finance Research Letters 2, 3 (2005), 125–130.
- FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs. arXiv preprint arXiv:2303.00859 (2023).
- Arbitrage-free neural-SDE market models. Applied Mathematical Finance 30, 1 (2023), 1–46.
- Rama Cont and José Da Fonseca. 2002. Dynamics ofimplied volatility surfaces. Quantitative finance 2, 1 (2002), 45.
- Rama Cont and Milena Vuletić. 2022. Simulation of arbitrage-free implied volatility surfaces. Available at SSRN (2022).
- Ashish Dhiman and Yibei Hu. 2023. Physics Informed Neural Network for Option Pricing. arXiv preprint arXiv:2312.06711 (2023).
- Bruno Dupire et al. 1994. Pricing with a smile. Risk 7, 1 (1994), 18–20.
- Jim Gatheral. 2011. The volatility surface: a practitioner’s guide. John Wiley & Sons.
- Flax: A neural network library and ecosystem for JAX. http://github.com/google/flax
- Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural networks 3, 5 (1990), 551–560.
- No-Arbitrage Deep Calibration for Volatility Smile and Skewness. arXiv preprint arXiv:2310.16703 (2023).
- Whack-a-Mole Learning: Physics-Informed Deep Calibration for Implied Volatility Surface. EasyChair Preprint 15219.
- Andrey Itkin. 2019. Deep learning calibration of option pricing models: some pitfalls and solutions. arXiv preprint arXiv:1906.03507 (2019).
- Diederik P Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014).
- Roger W Lee. 2005. Implied volatility: Statics, dynamics, and probabilistic interpretation. Recent advances in applied probability (2005), 241–268.
- A neural network-based framework for financial model calibration. Journal of Mathematics in Industry 9 (2019), 1–28.
- Physics-informed neural networks with hard constraints for inverse design. SIAM Journal on Scientific Computing 43, 6 (2021), B1105–B1132.
- Levi McClenny and Ulisses Braga-Neto. 2020. Self-adaptive physics-informed neural networks using a soft attention mechanism. arXiv preprint arXiv:2009.04544 (2020).
- Arbitrage-free implied volatility surface generation with variational autoencoders. SIAM Journal on Financial Mathematics 14, 4 (2023), 1004–1027.
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics 378 (2019), 686–707.
- Learning representations by back-propagating errors. nature 323, 6088 (1986), 533–536.
- DARE: The Deep Adaptive Regulator for Control of Uncertain Continuous-Time Systems. In ICML 2024 Workshop: Foundations of Reinforcement Learning and Control–Connections and Perspectives.
- An expert’s guide to training physics-informed neural networks. arXiv preprint arXiv:2308.08468 (2023).
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