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Short rate models are often classified as endogenous and exogenous. Endogenous short rate models are short rate models where the term structure of interest rates, or of zero-coupon bond prices (,), is an output of the model, so it is "inside the model" (endogenous) and is determined by the model parameters. Exogenous short rate models are ...
In financial mathematics, the Ho-Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates. [1]: 381 It was developed in 1986 by Thomas Ho [2] and Sang Bin Lee. [3] Under this model, the short rate follows a normal process:
The HJM framework originates from the work of David Heath, Robert A. Jarrow, and Andrew Morton in the late 1980s, especially Bond pricing and the term structure of interest rates: a new methodology (1987) – working paper, Cornell University, and Bond pricing and the term structure of interest rates: a new methodology (1989) – working paper ...
John Hull and Alan White, "One factor interest rate models and the valuation of interest rate derivative securities," Journal of Financial and Quantitative Analysis, Vol 28, No 2, (June 1993) pp. 235–254. John Hull and Alan White, "Pricing interest-rate derivative securities", The Review of Financial Studies, Vol 3, No. 4 (1990) pp. 573–592.
It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future evolution of all interest rates. It was the first model to combine the mean-reverting behaviour of the short rate with the log-normal distribution, [1] and is still widely used. [2] [3]
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As regards the short-rate models, these are, in turn, further categorized: these will be either equilibrium-based (Vasicek and CIR) or arbitrage-free (Ho–Lee and subsequent). This distinction: for equilibrium-based models the yield curve is an output from the model, while for arbitrage-free models the yield curve is an input to the model. [32]