Leveraging approximation properties of neural networks for efficient bond pricing

The purpose of this report is to examine the applications of deep learning-based approxi- mation techniques in the pricing of various financial instruments, with a particular emphasis on bond pricing methodologies. The report seeks to approximate pricing maps for bonds and options on the forward curve. Subsequently, the focus shifts to calibrating the input parameters by analyzing the observed prices. Finally, empirical evidence is presented to enable us to calibrate the input parameters of actual bond yields and observe the drift of these parameters as a proof of concept. This report implements the proposed methodology and applies it on three different pricing maps. Firstly, Chapter 3 touches upon the pricing of options on the forward curves for a given strike and maturity. Chapter 4 shifts the focus to the pricing of bonds, assuming the underlying short-rate follows a Vasicek process. Finally, Chapter 5 delves into the pricing of bonds with the short rate being composed of two different Vasicek-based control processes. Each of the aforementioned chapters focuses on the offline training of the model followed by an online calibration step of the input parameters conditional on the observed market price and the approximated pricing map. The bond-pricing chapters have an additional section to demonstrate the applicability of the pricing map in recovering the underlying parameters of the model by observing the empirical market bond price. This allows us to estimate how the underlying parameters of the assumed model drift with time at each time step.Bachelor of Science in Mathematical Sciences and Economic