I have an amortized bond with maturity at 30.04.2023, a semiannual frequency, 10% coupon rate, 30Е/360 day convention, and a clean price of 104.9367. Also, there are two amortization payments: 300 at 30.04.2018 and 300 at 30.04.2021. Assuming that today is 02.12.2019, what is yield to maturity?

My attempt:

I know that the formula is: $$P_{dirty} = \sum_i^N \frac{C/k}{(1+y/k)^i} + \frac{M}{(1+y/k)^N}$$ where y is yield to maturity, M is nominal of bond, N number of payment, k number of payments per year and C is yearly payment.

$P_{dirty}$ can be found using clean price and the accrued amount and then we can express y from this formula. But the question is, how to use it considering amortization payments. How do amortization payments affect C, M, and $P_{dirty}$?

  • 1
    $\begingroup$ What's "amortization payment 300"? 30% of the notional? In your formula, you need to include the amortization payments discounted the same way as the coupon payments. You can even add them up if they are on the same date. However, for the most general case, do not assume that amortization must happen on coupon dates, but allow them to happen anytime during coupon periods. Next, your coupon amount is wrong. Coupon is accrued on the notional remaining after amortization, not the initial notional. Finally, for accrued etc, do not use today (T+0, trade date), but settlement date, for which you $\endgroup$ Oct 3, 2021 at 14:01
  • $\begingroup$ must know the number of business days to settle (could be T+1, T+5, anything) and the settlement holiday calendar for this particular bond. $\endgroup$ Oct 3, 2021 at 14:03
  • $\begingroup$ One more thing: you can't just use i=1, 2,.., rather use cash flows' payment dates (unadjusted for holidays). $\endgroup$ Oct 3, 2021 at 19:06


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