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标题: effective convexity [打印本页]

作者: hoangvu90    时间: 2011-7-11 19:54     标题: effective convexity

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
作者: liquidity    时间: 2011-7-11 19:54

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




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