liquidity

$duration is -slope of price-yield curve. => duration is -slope/$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!