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Zero coupon bond key rate duration

zero coupon bond key rate duration

instruments off a zero or spot yield curve and used linear interpolation between " key rates but the idea is applicable to yield curves based on forward rates, par rates, and so forth. For large yield changes, convexity can be added to provide a quadratic or second-order approximation. Yrs.76.95 5 fixed-floating swap, Receive fixed 5 0 0 5 NA.79 All four have a 10-year maturity but the sensitivity to interest rates, and thus the risk, will be different: the zero - coupon has the highest sensitivity and the annuity. "Coping with the Risk of Interest- Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies." Lawrence Fisher and Roman. 1 where: idisplaystyle i indexes the cash flows, tidisplaystyle t_i is the time in years until the idisplaystyle i th payment will be received, Vdisplaystyle V is the present value of all cash payments from the asset. Finite yield changes edit Modified duration is defined above as a derivative (as the term relates to calculus) and so is based on infinitesimal changes. A bond with positive convexity will not have any call features -.e.

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zero coupon bond key rate duration

Bond, y has key rate durations.2 and.3 for these maturity points. A bond s coupon rate is a key factor in calculation duration. If we have two bonds that are identical with the exception on their coupon rates, the bond with the higher coupon rate will pay back.

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Reitano covered multifactor yield curve models as early as 1991 10 and has revisited the topic in a recent review. Then expression (2) becomes: V(y_k)sum _i1nPV_isum _i1nfrac CF_i(1y_k/k)kcdot t_i MacDsum _i1nfrac t_iV(y_k)cdot frac CF_i(1y_k/k)kcdot t_i To find modified duration, when we take the derivative of the value Vdisplaystyle V with respect to the periodically compounded yield we find 6 frac partial Vpartial y_k-frac 1(1y_k/k)cdot sum. Similar to the above, in these cases it may be more correct to calculate an effective convexity. Americas, europe, asia Pacific, contact your local office. Web browsers do not support matlab commands. The BPV will make sense for the interest rate swap (for which modified duration is not defined) as well as the three bonds. This will give modified duration a numerical value close to the Macaulay duration (and equal when rates are continuously compounded).