effective convexity

[cnd]

Can anybody please explain to me the derivation for the formula for effective convexity
Convexity = (V+ + V- - 2V0) / (2 x V0 x (Change in y)^2)
Many thanks

 

[cpk123]

not important…

 

[heatherw]

$duration is -slope of price-yield curve. => duration is -slope/$price
effective duration = (V+ - V-)/(V0*(2*change in y)). Note that as we change y symmetrically on both sides. Total change in yield is 2 times of delta y. (y+delta y) - (y - delta y) = 2*delta y.
convexity = slope of duration-yield=>
convexity = (D+ - D-)/(2*change in y)
D+ = ( V+ - V0)/(V0* change in y)
D- = (V0 - V-)/(V0*change in y)
substitute .
Hope this helps!