A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models
给出多因子HJM模型中即期利率过程为马尔可夫的充分条件，使贴现债券和利率期权能用标准模拟方法高效定价，数值实验表明模型能解释波动率微笑。
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 Sankarasubramanian (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).