In this chapter, we extend our study of interest rate models and practical implementations by focusing on advanced lattice methods and their applications in modern quantitative finance. We begin with the lognormal Hull–White (Black–Karasinski) model, a short-rate framework where the interest rate evolves lognormally, making it particularly suitable for pricing fixed-income securities and capturing realistic market dynamics. We will explore how to construct a lognormal Hull–White (BK) tree for bond pricing and then calibrate the model to both yield curves and volatility curves, ensuring consistency with observed market data.