7.25.2005

Q&A: Which is the Z-spread for...

...a 3.5-year, 9.60%, $100 par non-Treasury bond selling for 110.2950: 100 basis points, 143bp, or 165bp?

Period Spot Rate
1 0.03
2 0.033
3 0.035053
4 0.039164
5 0.044376
6 0.04752
7 0.049622

PV the cash flows (discounted at the appropriate spot rate + spread) and compare to the purchase price. The 143 Z-spread yields a purchase price of 4.70 + 4.58 + 4.46 + 4.32 + 4.15 + 4.00 + 84.08 = 110.2950.

  • Coupon = 9.6/2 = 4.8.
  • Coupon(i) PV = 4.8/(1+( Spot(i) + Z-spread)/2)^i
  • Period 1: 4.8/(1+(0.03+0.0143)/2) = 4.6960
  • Period 2: 4.8/(1+(0.033+0.0143)/2)^2 = 4.5808
  • Period 3: 4.8/(1+(0.035053+0.0143)/2)^3 = 4.4615
...
  • Period 7: (100+4.8)/(1+(0.049622+0.0143)/2)^7 = 84.0850

Category: C++ Quant > Debt > Valuation

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