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The Third Workshop on
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Heath-Jarrow-Morton Models with Regime-Switching Volatility
Mikael Elhouar
Abstract
This paper studies Heath-Jarrow-Morton (HJM) type of models with
regime-switching stochastic volatility.
In this setting the forward rate volatility is allowed to depend on
the current forward rate curve as well as
on a continuous time Markov chain $y$ with fintely many states.
Employing the framework developed by
Bjork et al, we find necessary and sufficient conditions on the
volatility that guarantee that the forward rate
process can be represented by a finite dimensional Markovian state
space model. These conditions allow
us to investigate regime-switching generalizations of some well-known
models such as those by Ho-Lee,
Hull-White, and Cox-Ingersoll-Ross.