Bond convexity closed-form formula

Bond convexity closed-form formula (Blake and Orszag[1]):

${\displaystyle Conv=-{\frac {D}{P}}{\begin{Bmatrix}{\frac {(m-1+a+1)(m-1+a+2)(1/(1+i))^{(m-1+a+2)}}{i}}+\\2{\frac {(m-1+a+2)(1/(1+i))^{(m-1+a+2)}-(1/(1+i))}{i^{2}}}+\\2{\frac {(1/(1+i))^{(m-1+a+2)}-(1/(1+i)}{i^{3}}}\end{Bmatrix}}+{\frac {B}{P}}{\frac {(m-1+a)(m-1+a+1)}{(1+i)^{(m-1+a+2)}}}}$

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