Mathematical models of market risk management used in banks

This thesis examines the performance and reliability of yield curve interpolation techniques during periods of monetary policy shifts and market turmoil. Chapter 1 establishes the foundational framework by exploring the evolution from IBOR-based single-curve approaches to modern OIS discounting within multi-curve frameworks, while presenting essential concepts of interest rate measurement and yield curve classification that underpin contemporary valuation methodologies. Chapter 2 develops the technical infrastructure by detailing bootstrapping procedures and interpolation techniques used in term structure construction, alongside examining regulatory requirements and practical applications that drive market risk assessment practices in modern banking environments. Chapter 3 presents the core empirical analysis, implementing a comprehensive methodology to evaluate how natural cubic spline interpolation, linear interpolation on zero rates, and linear interpolation on natural logarithm of discount factors perform under varying market conditions, particularly during central bank policy adjustments. The research challenges conventional assumptions about cubic spline superiority, demonstrating that simpler interpolation methods may provide greater stability and reliability during periods of market stress, ultimately contributing to more robust valuation frameworks for interest rate products.