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In the previous chapter, we explored the properties and analytics of single-factor interest rate models. For models like Vasicek, Cox–Ingersoll–Ross (CIR) and Hull–White, analytical formulas are available for bond prices and European options on bonds. However, in cases where closed-form solutions are unavailable, such as the Black–Derman–Toy (BDT) model, constructing an interest rate tree calibrated to market data—specifically, the current yield curve and the term structure of volatility—is essential for pricing interest rate derivatives.

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Short-Rate Models and Lattice Methods: Black–Derman–Toy, Hull–White, and FRA with QuantLib

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  • 发表日期：

    2025年

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  • Aaron De La Rosa

摘要

In the previous chapter, we explored the properties and analytics of single-factor interest rate models. For models like Vasicek, Cox–Ingersoll–Ross (CIR) and Hull–White, analytical formulas are available for bond prices and European options on bonds. However, in cases where closed-form solutions are unavailable, such as the Black–Derman–Toy (BDT) model, constructing an interest rate tree calibrated to market data—specifically, the current yield curve and the term structure of volatility—is essential for pricing interest rate derivatives.