General short-rate analytics

Short-rate models underlie the first steps of quantitative finance development. The main feature of such models consists of postulating the short-rate process. Vasicek (1977) and Hull & White (1990) pioneered a Gaussian short-rate model still popular among practitioners due to its analytical tractability and transparency. Black & Karasinski (1991) have proposed a lognormal short-rate model. Both models share the same Gaussian mean-reverting process but with different interpretations in terms of

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