YCM 2001 - Interpolation Techniques

# YCM 2001 - Interpolation Techniques - Interpolation...

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Copyright © 1996-2006 Investment Analytics Interpolation Techniques Slide: 2 Interpolation Techniques ± Why interpolate? ± Straight line interpolation ± Cubic spline interpolation ± Basis spline interpolation
Copyright © 1996-2006 Investment Analytics Interpolation Techniques Slide: 3 Why Interpolate ± Structuring ± Project security cash flows ± Need forward rates on coupon dates ± Valuation ± Need spot rates on coupon dates ± In either case coupon dates may not coincide with dates for which zero- coupon yields are known.

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Copyright © 1996-2006 Investment Analytics Interpolation Techniques Slide: 4 Interpolation Methods ± Straight Line ± Polynomial ± Single high order polynomial ± Unstable between points and at ends ± Splined polynomial ± Low order polynomials linked together ± Basis Splines ± Represent discount function as weighted sum of other functions
Copyright © 1996-2006 Investment Analytics Interpolation Techniques Slide: 5 Straight Line Interpolation – Pros and Cons ± Simple to estimate intermediate points on curve ± Not accurate for undulating curves ± Gives different results on discount factors ± Produces discontinuous forward rate curve

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Copyright © 1996-2006 Investment Analytics Interpolation Techniques Slide: 6 Linear Interpolation ± Intermediate values lie on a straight line between the nearest data points. ± R i = R 1 + (R 2 -R 1 ) x (T i -T 1 ) / (T 2 1 ) T 1 T i T 2 R 1 R i R 2
Copyright © 1996-2006 Investment Analytics Interpolation Techniques Slide: 7 Linear Interpolation: Rates or Discount Factors? ± If interest rates lie on a straight line, discount factors do not ± Example: ± Using Rates Using DF’s R 1 = R2 = 5.00% D 1 = 0.9877 T 1 = 90 D 2 = 0.9756 T 2 = 180 D i = 0.9836 T i = 120 R i = 5.00% R i = 4.99%

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Copyright © 1996-2006 Investment Analytics Interpolation Techniques Slide: 8 Linear and Exponential Interpolation ± Linear interpolation on continuously compounded interest rates is equivalent to exponential interpolation on discount factors De D e RR R TT DD D RT i i i T T T T ii 1 12 1 21 1 1 2 11 2 2 2 1 = = =− + = ⇒= , () αα α
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## YCM 2001 - Interpolation Techniques - Interpolation...

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