This thesis investigates the application of neural stochastic differential equations (NSDEs) in financial modeling. It begins by presenting existing theoretical interpretation of NSDEs and investigates the properties of their solutions. By establishing a solid foundation, the thesis sets the stage for further explorations. A significant focus of the research is on the calibration and joint calibration of options using Markovian-type neural SDEs. This modeling approach is carefully chosen after conducting an extensive analysis that considers both the supporting evidence for the rough volatility hypothesis and the counterarguments in favor of Markovian volatility models. By undertaking a thorough study of these perspectives, the thesis aims to provide an in-depth understanding of the advantages and disadvantages associated with each modeling approach.
Additionally, the thesis addresses the challenge of data scarcity, a common issue faced in financial research. Recognizing the limited availability of real-world data and its potential impact on model development and testing, the research explores various existing methods for generating synthetic financial data.