Bond duration closed-form formula

From Reuters Financial Glossary

Bond duration closed-form formula (Richard Klotz) (http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fpages.stern.nyu.edu%2F~msiegel%2FUnderstandingDuration.doc&ei=usfLRp65Lon2hQPq8PT6CQ&usg=AFQjCNEBCNz1CXJOO8VOVCMfYvyPysnxUA&sig2=Wk2Bb7Db8_jUeZSN4baGcg):

Dur=\frac{C\frac{(1+ai)(1+i)^m-(1+i)-(m-1+a)i}{i^2(1+i)^{(m-1+a)}}+\frac{100(m-1+a)}{(1+i)^{(m-1+a)}}}{P}


C = coupon payment per period (half-year)
i = discount rate per period (half-year)
a = fraction of a period remaining until next coupon payment
m = number of coupon dates until maturity

Look up Bond convexity closed-form formula

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