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adoDojo
adoDojo
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adoDojo
adoDojo
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Price of Bond with irregular long first coupon period

I'm trying to manually calculate the price of a bond with a long first coupon period, found a few candidate formulas on

Microsoft Excel Document: OddFPrice

mit.edu: OddFPrice

WestClinTech.com: Calculating price of bond with OFC on SQLServer

The presented formulae vary across these sources, also I can't seem to match the results given by the software when using the formula given for it (microsoft excel for instance). I suspect my current problem is an unclear understanding of the variables used in the calculations. The following is a brief description of my current mental model (using notation on excel):

Example Problem Data:

  • Bond Issue Date(m/d/y): 10 / 15 / 2008
  • Settlement Date: 11 / 11 / 2008
  • First Coupon Date: 1 / 1 / 2010
  • Maturity Date: 1 / 1 / 2022
  • Coupon Rate: 7.85%
  • Frequency of coupon payments: semi-annual
  • Yield: 6.25
  • Redemption Value per $100 face-value: $100
  • Day count basis: Actual/actual

Current understanding of the terms (as described in the given equation on excel page)

  • Ai: Number of days from bond issue date to settlement date
  • DCi: Number of days from issue date to next imaginary coupon after issue date (not first actual coupon)
  • DSC: Number of days from settlement date to next imaginary coupon after issue date (not first actual coupon)
  • E: Length in days of the first coupon period
  • N: Number of coupons payable between the first coupon date(exclusive) and maturity date
  • NC (becomes hairy here I think): Number of imaginary coupons between the issue date and settlement date
  • NLi: Length in days of the imaginary coupon period which happens to contain the settlement date
  • Nq: Number of imaginary coupon periods between settlement date and first coupon date rounded down

I strongly suspect my grasp of these terms is the real problem, so I'd very much appreciate any of the following:

  1. Clarification on the terms I described or confirmation if correct
  2. The correct/preferred formula of the three sources
  3. A detailed explanation of the problem solving process

NB: I used the term 'imaginary coupon' here in place of quasi or pseudo coupon, I do not clearly understand the meaning of those terms in these context, or whether they mean the same thing, a clarification would also be appreciated greatly.

I'm happy to provide additional details if required, thanks.