Two-factor Black-Karasinski pricing kernel

Analytic formulas for bond prices and forward rates are derived by expanding existing rate models

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Colin Turfus and Alexander Shubert present an analytic pricing kernel for a two-factor Black-Karasinski (lognormal) short-rate model as a rapidly convergent perturbation expansion valid in the limit of low rates. This expansion is used to derive analytic formulas for conditional bond prices and forward rates. The model is equally applicable to modelling credit spreads, and it satisfies the important requirement of guaranteeing positive implied default probabilities

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