Bond Duration Formulas
For a standard bond with fixed, semi-annual payments the bond duration closed-form formula is:
- FV = par value
- C = coupon payment per period (half-year)
- i = discount rate per period (half-year)
- a = fraction of a period remaining until next coupon payment
- m = number of full coupon periods until maturity
- P = bond price (present value of cash flows discounted with rate i)
For a bond with coupon frequency but an integer number of periods (so that there is no fractional payment period), the formula simplifies to:
where
- y = Yield (per year, in decimal form),
- c = Coupon (per year, in percent),
- m = Number of coupon periods.
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