# Bond duration closed-form formula

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Bond duration closed-form formula

Bond duration closed-form formula:

$Dur=frac\left\{Cfrac\left\{\left(1+ai\right)\left(1+i\right)^m-\left(1+i\right)-\left(m-1+a\right)i\right\}\left\{i^2\left(1+i\right)^\left\{\left(m-1+a\right)+frac\left\{100\left(m-1+a\right)\right\}\left\{\left(1+i\right)^\left\{\left(m-1+a\right)\right\}\left\{P\right\}$

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 coupon dates until maturity

Look up Bond convexity closed-form formula

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