Which of the Following Is a Required Property of the Cubic

question 6

Multiple Choice

Which of the following is a required property of the cubic spline approach to estimating the yield curve and discount functions $d ( t )$ ? Recall that the approach fits functions $d _ { k } ( t )$ to $k$ regions between $( k + 1 )$ knot points.

• A) \(d ( 0 ) > 1\)
• B) \(d _ { k } \left( T _ { k + 1 } \right) = d _ { k + 1 } \left( T _ { k + 1 } \right)\)
• C) \(d _ { k } ^ { \prime } \left( T _ { k + 1 } \right) > d _ { k + 1 } ^ { \prime } \left( T _ { k + 1 } \right)\)
• D) \(d _ { k } ^ { \prime \prime } \left( T _ { k + 1 } \right) < d _ { k + 1 } ^ { \prime \prime } \left( T _ { k + 1 } \right)\) where \(d ^ { \prime } ( t )\) and \(d ^ { \prime \prime } ( t )\) denote first and second derivatives of the function \(d ( t )\) with respect to \(t\) .

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Definitions:

Peripheral Countries

Nations that are less economically developed with minimal influence in the global economic system, often exploited by more dominant, economically powerful countries.

Taiwan

An island in East Asia, known for its dynamic economy and vibrant democracy, despite complex international status and relations with China.

South Korea

A country located in East Asia, known for its advanced technology and vibrant culture, officially called the Republic of Korea.