Question

Consider a bond with maturity 4 year, 100 face value, coupon 5%, and yield 5%. Compute a dollar duration numerically using a dy-0.001%. Recall that $Dur is approximately equal to [Ply+dy)-P(y)]/dy when dy is small and Pſy) is the price of the bond at the yield y.

Answer 1

Face value = $100
Maturity period = 4 years
Coupon = 5%
Yield = 5%
dy = 0.001%

$Dur = [p(y+dy) - P(y)]/dy = [P(5.001) - p (5)]/0.001

Price of bond at yield y = (Face value /(1 + yield)^ maturity period) + (Coupon payment per period * (1 - (1+yield)^-maturity period)/yield

P(5.001) = $100/(1.05001)^4 + [$5 * (1-(1.05001)^-4)/0.05001] = $99.996454
P(5) = $100/(1.05)^4 + [$5 * (1-(1.05)^-4)/0.05] = $100

$Dur = [$99.996454 - $100]/0.001 = -$3.5459