Let Two Time Points $t _ { 1 }$ And $t _ { 2 }$

Let two time points, $t _ { 1 }$ and $t _ { 2 }$ ,on a yield curve be given,and let $y \left( t _ { 1 } \right)$ , $y \left( t _ { 2 } \right)$ be the yields at these maturities.You want to draw an interpolating curve between these maturities and are considering three alternatives: -Linear (L) :
-- $y ( t ) = y \left( t _ { 1 } \right) + x \cdot \left( t - t _ { 1 } \right)$ --.
-Exponential (E) :
-- $y ( t ) = y \left( t _ { 1 } \right) e ^ { x \left( t - t _ { 1 } \right) }$ --.
-Logarithmic (G) :
-- $y ( t ) = y \left( t _ { 1 } \right) \left[ 1 + \ln \left( 1 + x \cdot \left( t - t _ { 1 } \right) \right) \right]$ --.
Since the interpolated curves will not coincide perfectly except at the two end-points,interpolated yields will be higher under some methods versus the others.What is the rank-ordering of size of interpolated yields?

A) $L < E < G$
B) $E < G < L$
C) $G < L < E$
D) $E < L < G$

Correct Answer:

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