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摘要
The Hull-White model is a one factor Markov model well known for its capability to capture the current term structure of interest rates. Analytical results are available for pricing zero-coupon discount bonds and associated European options when both reversion and volatilityfunctions are constant. In reality, however, these functions do vary over time. It is then of practical interest to develop efficient computational algorithms that can deal with time dependent reversion and volatility functions. The purpose of this article is to achieve this goal via the Ehrenfest approximation of the underlying O-U process, where the time dependent structure is represented by step functions. Based on the convergence theorem by Sumita, Gotoh and Jin [2006] and the uniformization procedure of Keilson [1979], a novel approach is proposed to evaluate the prices of zero-coupon discount bonds and associated European options for stepwise reversion and volatilityfunctions. The ordinary Hull-White trinomial tree approach is also modified to cope with this case for comparison purposes. However, it is shown that the modified trinomial tree approach is not applicable for certain step functions, while the Ehrenfest approach can always be used for any step functions. Numerical results are given, demonstrating the excellent speed and accuracy of the Ehrenfest approach.
- 出版日期2007
- 单位杭州电子科技大学
