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

question 2

Multiple Choice

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) \(E < L < G\)

---

Definitions:

Consumer Surplus

The difference between what consumers are willing to pay for a good or service and what they actually pay, representing the benefit consumers receive.

Producer Surplus

The difference between what producers are willing and able to supply a good for and the price they actually receive, measuring the benefit to producers.

Total Surplus

The total net gain to society from creating and consuming a product or service, encompassed by the combination of consumer and producer surplus.

Deadweight Loss

An inefficiency in the economy that results when the market equilibrium for a good or service isn't attained or is unattainable.