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Heath-Jarrow-Morton model
       
 
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Heath-Jarrow-Morton model

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Heath-Jarrow-Morton model
A multi-factor Interest rate model, which describes the dynamic of Forward rate evolution. An extension of the Ho-Lee model, the Underlying is the entire term structure of Interest rates. The approach is very similar to the original Black-Scholes model: it does not model qualities such as the ‘price for Risk’. The model requires two inputs: the initial Yield curve and a Volatility structure for the Forward. The Volatility is only specified in a very general form. By choosing an appropriate Volatility function, it is possible to reduce HJM to simpler models such as Ho-Lee, Vasicek, and Cox-Ingersoll-Ross. The practical importance of the HJM model is that it provides a single coherent framework for pricing and Hedging an entire book of instruments (including instruments such as caps and swaptions) and is not excessively computationally intensive. Research building on HJM (such as the market model) has concentrated on widening its scope to remove the possibility of negative Interest rates, include more than one Interest rate curve and incorporate Default Risk.
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