Physics-informed neural network for barrier option pricing in coupled financial quantitative system with varying interest rate and volatility

Accurate pricing of barrier options is essential for facilitating informed investment decisions, optimizing resource allocation, and promoting market stability. The dynamics of interest rate and volatility significantly influence the barrier option pricing. Traditional equations associated with constant parameters may fail to capture these complexities. In this paper, the underlying asset is assumed to follow an extended geometric Brownian motion incorporating varying interest rate and volatility, and then a coupled pricing system for the up-and-out call option is derived based on the Kolmogorov forward equation and backward equation, enabling the analysis of volatility fluctuations. Higher volatility indicates a greater level of risk, which may correspond to higher potential returns. The fusion framework, the physics-informed neural network (PINN), is introduced to solve this coupled system, consisting of two subnetworks: one dedicated to estimating the expected values of barrier option prices, and another for capturing the volatility surface associated with the option prices. Experimental results based on the closing price data of CSI 300ETF options show that PINN offers an effective and efficient framework for evaluating the prices of financial derivatives, achieving high precision and interpretability, even in cases where closed-form analytical solutions are unavailable.