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I'm getting confused about how I should price the current price of a zero coupon bond when there are several yields to choose from. For instance, lets say that there is an upward sloping yield curve. The rates are $r_1 < r_2 < \cdots < r_{10}$.

Typically, when we price the current price of zero coupon bond that matures in 1 year, the calculation is simply $$ P = \frac{100}{1 + r_1} $$ However, when we price the current price of a 10 year zero coupon bond, I feel that it is overly simplistic to calculate the price as $$ P = \frac{100}{(1+r_{10})^{10}} $$ Rather, I feel that the correct way to price this is to think the rates as forward rates for each year so that $$ P = \frac{100}{(1+r_1)(1+r_2) \cdots (1+r_{10})} $$

Any input will be much appreciated. Thanks in advance.

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    $\begingroup$ The yield curve can be expressed in several ways. What are these $r_i$s ? ZCB rates or forward rates? Where did you get them? If ZCB rates then the 1st answer, otherwise the secon. $\endgroup$ – Alex C Apr 3 '17 at 0:03
  • $\begingroup$ There is even a third possibility the $r_i$s could be the "par rates". $\endgroup$ – Alex C Apr 3 '17 at 0:41
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Your approach is correct, but the practical difficulty is that you do not see zero-coupon spot rates for maturities longer then 1 year; and zero-coupon spot rates are the relevant rates for pricing zero-coupon bonds.

So 10 year zero-coupon spot rate curve needs to be bootstrapped from other bonds but in practice there are no 10 year zero-coupon bonds traded so this exercise has only theoretical meaning.

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