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dejiazheng · 2024年04月18日

是否向上的收益率曲线都满足f(2,1)>f(1,2)>f(1,1)

NO.PZ2023040701000004

问题如下:

Consider spot rates for three zero-coupon bonds: r(1) = 3%. r(2) = 4%. and r(3) = 5%. Which statement is correct? The forward rate for a one-year loan beginning in one year will be:

选项:

A.

less than the forward rate for a one-year loan beginning in two-years.

B.

greater than the forward rate for a two-year loan beginning in one-year.

C.

greater than the forward rate for a one-year loan beginning in two-years.

解释:

Correct Answer: A

The forward rate for a one-year loan beginning in one-year f(1,1) is

The rate for a one-year loan beginning in two-year f(2,1) is .This confirms that an upward sloping yield curve is consistent with an upward sloping forward curve.

印象中曾说过不同起始时间点的forward rate不能比较,因为不在同一条找上。但何老师在经典题视频却放在一起比较,请老师指教

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吴昊_品职助教 · 2024年04月19日

嗨,爱思考的PZer你好:


forward curve有很多条,f(1,1)和f(1,2)...f(1,n)是在同一条forward curve上,f(2,1)和f(2,2)...f(2,n)是在另一条forward curve上。

如果当即期利率曲线向上倾斜,那么forward rate curve也是向上倾斜的,并且forward curve在spot curve上方。站在2时间点的forward curve位于站在1时间点的forward curve的上方。也就是下方图中,绿色曲线在红色曲线上方,红色曲线在黑色曲线上方。只要绿色曲线在红色曲线上方,就代表f(2,1)在f(1,2)上方。综合比较就能得到f(2,1)>f(1,2)>f(1,1)

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