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The price of a bond can vary because:

  • the yield curve changes

  • the flow of time (the time to maturity is reducing, for example compare a 1 year ZC bond with a 0.5 year ZC bond)

How can I quantify the effect of each precisely?

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Modified Duration and Convexity measure a bond's first- and second-order sensitivity to yields. With small changes in yield, duration is often sufficient since the change due to convexity will be much smaller. With larger yield changes, convexity can have a impact.

Sensitivity to time is more complicated mathematically, and there's not as much practical application, but in general, bonds tend to move toward par (100%) as time passes, all else being equal. So if the current price is close to par, there won't be much sensitivity to time passing.

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There is no way to write anything in mathematical notation on this exchange. If it were me I would either construct regressions using the method of maximum likelihood or a Bayesian method because you could incorporate the present value formula directly in the regression. You cannot run separate regressions because it would be inaccurate.

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Consider Bond A and Bond B both with the same coupon and the same redemption date. But send Bond B forward in time as closer to redemption.

Calculate the price of the Bond A with the yield of Bond B and note the change in price. Then calculate the price of the original Bond A with the remaining time of Bond B and note the change in price.

The results begin two separate graphs. One graph of Bond A price changing with yield and another graph of Bond A price changing with time.

Calculating bond price is not too difficult. Calculating yield from bond price is more difficult and therefor I previously posted an alternative bond pricing method that has a direct inverse. But an alternative bond pricing only works within its own system.

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