The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims
The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims
复制标题
DOI：
10.1111/1467-9965.00110
复制
发表时间：
2001-01
影响因子：
1.6
通讯作者：
N. Kunitomo;Akihiko Takahashi
中科院分区：
文献类型：
--
作者：
N. Kunitomo;Akihiko Takahashi
当标的资产价格遵循一般类别的连续 Itô 过程时，我们提出了一种新的方法来解决金融或有债权的估值问题。我们的方法可以应用于广泛的估值问题，包括与利率期限结构相关的复杂或有债权。我们通过举两个例子来说明我们的方法：掉期期权和平均（亚洲）利率期权的估值问题。我们的方法给出了一些明确的解决方案公式，这些公式在大多数情况下对于实际目的来说足够精确。即期利率和远期利率的连续随机过程不一定是通常意义上的马尔可夫过程或扩散过程；然而，我们的方法可以通过随机分析中的 Malliavin-Watanabe 微积分来严格证明。
We propose a new methodology for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. Our method can be applied to a wide range of valuation problems including complicated contingent claims associated with the term structure of interest rates. We illustrate our method by giving two examples: the valuation problems of swaptions and average (Asian) options for interest rates. Our method gives some explicit formulas for solutions, which are sufficiently numerically accurate for practical purposes in most cases. The continuous stochastic processes for spot interest rates and forward interest rates are not necessarily Markovian nor diffusion processes in the usual sense; nevertheless our approach can be rigorously justified by the Malliavin–Watanabe Calculus in stochastic analysis.