Bond convexity closed-form formula


Bond convexity closed-form formula

Bond convexity closed-form formula (Blake and Orszag): Conv=-frac{D}{P}egin{Bmatrix}frac{(m-1+a+1)(m-1+a+2)(1/(1+i))^{(m-1+a+2){i}+\2frac{(m-1+a+2)(1/(1+i))^{(m-1+a+2)}-(1/(1+i))}{i^2}+\2frac{(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

Look up Bond duration closed-form formula


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