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For a bond with market price $P_t$ and fixed payments $c_n$, I'm told the yield to maturity is given by the solution $Y$ to the equation

$P_t=\sum_{n=1}^N c_n e^{-Y(t_n-t)}$.

Firstly, I'm not great a rearranging such equations to not sure how to find an expression for $Y$ from here.

Also could someone explain what each $t_n$ is? As in, in the equation what's the difference between the fixed $t$ and the $t_n$?

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1 Answer 1

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I think $t_n$ is the time the nth coupon is paid and $t_n$-t is the time difference between the time the coupon is paid at the time the bond is issued.

So if a bond is issued on May 10 and coupons are paid on June 10, July 10 and August 10, then the $t_n$ - t's are 1/12, 2/12 and 3/12.

Y cannot be solved directly. It's like Internal Rate of Return. Use Goal Seek in Excel.

https://ph.answers.yahoo.com/question/index?qid=20081123061034AA419b4 YTM: http://www.youtube.com/watch?v=NV0S8pKvje8 Goal Seek: http://www.youtube.com/watch?v=7QIBvMPC9vM

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Ok I didn't think Y could be solved directly just from looking at it. $t$ has units months? Not as ratios of one year? –  user13223423 May 10 at 14:09
    
Mea culpa. 1/12, 2/12, 3/12 –  BCLC May 10 at 14:10
    
@user13223423 Out of curiosity, what is your reference material? Just wondering since Hull's OFOD uses t instead of $t_n$-t –  BCLC May 10 at 16:05

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