Bond Pricing Under Sticky OU Process

In this paper, we derive the conditional characteristic function of the sticky Ornstein-Uhlenbeck (OU) process and explore bond pricing under this framework. We systematically transform the standard OU process into the sticky OU process by incorporating the time-varying symmetric local time, thereby establishing the existence of a unique weak solution for this modified process. Subsequently, leveraging the infinitesimal generator and its domain, we meticulously compute the conditional characteristic function of the sticky OU process. Following a similar analytical approach, we incorporate the sharpe ratio into our bond pricing methodology, ensuring coherence and rigor in our calculations. Notably, all our findings are presented in closed-form expressions, facilitating straightforward interpretation and application in financial modeling and analysis. This comprehensive treatment not only advances the theoretical understanding of the sticky OU process but also offers practical insights into bond valuation dynamics under this intricate process.