[讨论]TAR和Vasicek model

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今天在看TAR的时候发现,它可以转化成一个有条件的扩展的Vasicek model,即dr=a(b-r)dt+sigma*dw中的a在r>b和r<b的时候的取值不同,这个在利率结构里面不知道是否符合,但是在美国的股市收益率似乎是符合的(向下的幅度大于向上的幅度,这样就意味着回归平均收益率的速度是不同的),的不知道学术界有没有这类的随机过程的模型呢?

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关键词：Vasicek model mode ASIC ASI 讨论 model Vasicek TAR

dynamics of short rate(nonlinearity in drift)

let's talk the drift only, coz u didn't mention the diffusion term.

different studies find different results of relationships between the mean-reverting speed and the short rate dynamics. For example, Ait-sahalia(1996) and Conley et al.(1997)find evidence of strong mean reversion when r(t) is below the 2% normal range [U-shaped function of mena reversion], while others like Stanton(1997)argues no evidence of strong mean reverting at low level interest rates, among which Ahn and Gao(1999) defined a quadratic nonlinear model of the drift term[dr(t)=a(b-r(t))r(t)+...], which assumes the mean reverting speed increases linearly with the short rate.

for detailed descriptions of the nonlinearity of interest rate term structure model, please go through the references list above. i hope it could help.

Thanks for ur advices

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