Heath-Jarrow-Morton Model

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Heath-Jarrow-Morton Model

A model that uses forward interest rates to determine prices for securities that are affected by changes in interest rates. The model is quite complex and used mainly by arbitrageurs. It may also be used in asset liability management.
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For example, Cairns, Blake, and Dowd (2006) consider a two-factor model; Bauer, Boerger, and Russ (2008) use a model that is parallel to the HJM model for interest rates.
Pricing Asian Interest Rate Options with a Three-Factor HJM Model.
Finally, if we model forward rates as log-normal processes the HJM model will explode (2).
So, by construction, the HJM model fits the initial term structure exactly.
In order to price Euribor interest rate caps, we estimate a restrictive HJM model via the Kalman filter.
In the next section, we show how the one-factor HJM model can be expressed in a state space form and can be estimated by the Kalman filter technique.
The HJM models are estimated with specific volatility functions to ensure that the interest rate process is Markovian, i.
2010) implemented the HJM model (Heath et al, 1992) for ID options, which generalizes both the Vasicek and CIR models.
Alternatively, the HJM model considers the forward-rate as the basic ingredient in modeling the interest rate evolution.
In order to implement the HJM model, one has to specify the volatility structure of forward rates.
To this end, we use the HJM model with the volatilities of the instantaneous forward rates computed by the factor loadings and the volatilities of the independent factors.
This could mean that the models used by market agents to price these options simplify the interest rate volatility structure to only one component or that the market price of IDI options (4) may not be an appropriate measure to quantify the quality of the HJM model.