Macro-driven ultimate forward rates and long-term interest rates

This paper develops a macro-driven framework that endogenously determines the Ultimate Forward Rate (UFR) for long-term interest rate extrapolation. Unlike the Smith–Wilson method, which assumes an exogenous UFR, our approach derives it from a heterogeneous-agent overlapping generations model that incorporates structural features such as productivity growth, employment risk, and fiscal policy. The derived UFR is then applied within the Smith–Wilson method to extrapolate the yield curve. Simulations show that this approach produces long-term rate projections more closely aligned with macroeconomic fundamentals. Model calibration using German and Japanese data highlights the role of demographic ageing and fiscal pressures in shaping the long end of the yield curve, emphasizing the structural nature of long-term interest rate determination. These results have practical implications for settings where discount rates critically affect liability valuation. Anchoring the UFR in economic fundamentals offers a more transparent and justifiable basis for long-term rate setting, particularly in insurance and pension contexts.