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Quantitative Finance · Glossary

What is Black–Karasinski model?

Also known as: Black--Karasinski model

Definition 7.7 Rates, Credit, XVA and Risk · Chapter 7 — Short-Rate Models

The Black–Karasinski model (1991) makes the logarithm of the short rate mean-reverting and normal, dln⁡rt=(ϑ(t)−κln⁡rt) dt+σ dWtd\ln r_t = (\vartheta(t)-\kappa\ln r_t)\,dt+\sigma\,dW_t: rates stay positive, bond prices have no closed form, and the model is used on trees. It lost ground when rates went negative.

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