D = coupon payment per period
P = present value (price)
B = face value
i = discount rate per period (half-year)
a = fraction of a period remaining until next coupon payment
m = number of coupon dates until maturity
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Bond duration closed-form formula — Bond duration closed form formula:Dur=frac{Cfrac{(1+ai)(1+i)^m (1+i) (m 1+a)i}{i^2(1+i)^{(m 1+a)+frac{100(m 1+a)}{(1+i)^{(m 1+a)}{P}C = coupon payment per period (half year) i = discount rate per period (half year) a = fraction of a period… … Wikipedia
Closed-form formula — A single arithmetic formula obtained to simplify an infinite sum in a general formula. The general formula of bond duration and bond convexity cannot be said closed form as there is an infinite sum over the different time periods. Using a closed… … Wikipedia
Bond duration — Financial markets Public market Exchange Securities Bond market Fixed income Corporate bond Government bond Municipal bond … Wikipedia
