Whack-a-mole Online Learning: Physics-Informed Neural Network for Intraday Implied Volatility Surface

TL;DR

This paper introduces WamOL, a physics-informed neural network method for real-time calibration of the intraday implied volatility surface, effectively handling sparse data and complex constraints in computational finance.

Contribution

The paper presents a novel PINNs-based approach with adaptive loss balancing for intraday IVS calibration, improving accuracy and efficiency over existing methods.

Findings

WamOL outperforms traditional calibration methods on sparse market data.

The approach accurately captures the dynamic evolution of IVS intraday.

WamOL effectively integrates PDE and no-arbitrage constraints in real-time.

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.