I know they most likely will only ask us annual or semi-annual compounding with a duration/convexity problem but rather than memorize that we have to multiply ages by 2 and divide by 4 (or something like that), I'd rather look at the actual derivation and formula. So...
What is the general formula for convexity? I believe it's the weighted average of t(t+(1/k)) with the same PV(CFi)/Price weights as in duration, all divided by (1+(y/k))^2. Is this correct? Here is my math.
P = sum of CFi (1+y/k)^-ik
P' = sum of -i CFi (1+y/k)^(-ik-1)
P'' = sum of -i(-ik-1) CFi [(1+y/k)^(-ik-2)] (1/k).
= sum of i(i+1/k) CFi [(1+y/k)^(-ik-2)]
= sum of i(i+1/k) CFi [(1+y/k)^(-ik)] divided by (1+y/k)^2
Thanks in advance!
What is the general formula for convexity? I believe it's the weighted average of t(t+(1/k)) with the same PV(CFi)/Price weights as in duration, all divided by (1+(y/k))^2. Is this correct? Here is my math.
P = sum of CFi (1+y/k)^-ik
P' = sum of -i CFi (1+y/k)^(-ik-1)
P'' = sum of -i(-ik-1) CFi [(1+y/k)^(-ik-2)] (1/k).
= sum of i(i+1/k) CFi [(1+y/k)^(-ik-2)]
= sum of i(i+1/k) CFi [(1+y/k)^(-ik)] divided by (1+y/k)^2
Thanks in advance!
General Convexity formula
