Neural Conformal Inference for jump diffusion processes

Abstract

Bayesian inference for jump diffusion processes (JDPs) remains challenging due to intractable transition densities and the latency of jump times and intensities. This paper introduces Neural Conformal Inference for JDPs (NCoin-JDP), a novel likelihood-free approach that leverages the power of deep neural networks (DNNs). NCoin-JDP bypasses the limitations of traditional methods by establishing a direct mapping between observed data and model parameters using a DNN. This approach eliminates the discretization errors inherent in likelihood-based methods, leading to more accurate inference. Despite the black-box nature of DNNs, we establish the asymptotic theory to quantify the approximation error of our algorithm. Additionally, we calibrate the uncertainty of our estimations using conformal prediction, providing theoretical guarantees of equivalence with the Bayesian posterior. NCoin-JDP demonstrates competitive performance compared to state-of-the-art methods. We showcase its effectiveness through numerical simulations and apply it to real-world data (S&P 500 and NASDAQ, 1993–2024) to investigate the impact of COVID-19 on the US economy. All numerical studies are reproducible in https://github.com/anonymous1116/NCoin-JDP.