Liang, Jiaqi; (2025) Fourier transform and machine learning methods for the pricing of discretely monitored barrier options. Doctoral thesis (Ph.D), UCL (University College London).

Preview

Text Liang_10217631_Thesis.pdf Download (6MB) | Preview

Abstract

Discretely monitored barrier options, observed only at specific monitoring dates, are common in practice but pose significant challenges to pricing due to their path dependence and the complexity introduced by discrete monitoring. This thesis develops efficient and accurate methods for pricing discretely monitored barrier options under the Heston stochastic volatility model, which captures important market features such as volatility clustering and the implied volatility smile. Leveraging the Heston model’s tractable characteristic function, two novel Fourierbased methods are proposed: the Fourier z-transform method (FZ), based on an extension of the Wiener-Hopf technique, and the recursive Fourier-Hilbert transform method (FH). To support these techniques, the thesis includes a detailed analysis of two formulations of the joint conditional characteristic function of the Heston model, resolving discontinuities and ensuring numerical stability. Extensive numerical experiments validate the robustness and accuracy of the proposed methods across a wide range of parameter regimes, including challenging cases. The thesis also explores the use of deep learning to approximate option prices. A neural network model is trained on data generated by the FZ method and demonstrates strong predictive performance, offering a scalable, data-driven alternative for pricing and calibration. By combining analytical tractability, numerical efficiency, and machine learning, this thesis provides practical and adaptable tools for pricing discretely monitored barrier options.

Download activity - last month

Export as JSONXMLCSV

Download activity - last 12 months

Export as CSVXMLJSON

Downloads by country - last 12 months

Export as CSVXMLJSON

Archive Staff Only

View Item