A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models

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Abstract
We consider the general n-factor Heath, Jarrow, and Morton model (1992) and provide a sufficient condition on the volatility structure for the spot rate process to be Markovian with 2n state variables. The price of a discount bond is also Markovian with the same state variables and, hence, claims against the term structure can be efficiently priced using standard simulation techniques. Our results extend earlier works such as Ritchken and Sankara-subramanian (1995) where the one-factor model is treated, and Carverhill (1994), where the volatility structure is non-random. Numerical experiments show that our model can explain the volatility smile observed in the interest rate options market and also overcome the biases noted by Flesaker (1993).

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