Pricing of Bonds Under Interest Rate Models with Bimodal Densities

This paper investigates the valuation of fixed-income securities under short-rate dynamics characterised by bimodal probability distributions. In particular, the valuation of zero-coupon bonds under short-rate dynamics provides one of the fundamental links between a model of interest rates and observable prices of fixed-income securities. Traditional term structure models, such as affine diffusion and single-regime stochastic processes, typically assume unimodal distributions for interest rates, limiting their ability to capture environments with persistent clustering around distinct rate levels. Motivated by empirical observations of policy-driven regimes and liquidity segmentation in modern money markets, we introduce a framework in which the short rate exhibits bimodal density that does not rely explicitly on a regime-switching mechanism. We develop a tractable pricing methodology for zero-coupon bonds under this setting, calibrate the solution to real data and numerically validate the solution. We also examine how bimodality influences yield curves. The analysis highlights that bimodal distributions can generate non-standard term-structure shapes that differ from classical models.