Safe Havens in Times of Crisis: A Mathematical and Quantitative Study of Gold and Bonds

This thesis aims to investigate the role of safe haven assets during periods of economic and financial crisis, focusing on two instruments traditionally viewed as secure: gold and government bonds. After introducing the necessary mathematical foundations, such as stochastic processes, Brownian motion, and jump models, the study develops a theoretical framework for modeling asset price dynamics. Particular attention is given to interest rate modeling, including a detailed exploration of the Vasicek model and its application to bond pricing. The final part of the thesis will include an empirical analysis using historical data, comparing the performance of gold and sovereign bonds during past crises. The goal is to assess which of the two assets has historically behaved as a more reliable safe haven in times of market turmoil.