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I understand that for US treasury bonds, that the price, its current yield and annual coupon is related by

price = coupon/yield.

But the prices and yields when I look them up online are always denoted for fixed periods such as 1 month, 3 month, 6 month, 12 month, 1 year, 2 year, 5 year, 10 year, 30 year and so on.

How can I find out (calculate or otherwise determine) the price on at a time after the bond was issued when falls in between any such period? Say I have a bond that matures in 3 years, 2 months, 2 weeks, 3 days, 3 hours 2 minutes, 4 seconds? How would I find out the current market price from first principles?

Mikkel Rev
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There isn't a simple formula. The selling price depends on what interest rate new bonds are offering or are likely to offer, compared with the rate on this bond and the remaining time on it. So it becomes a matter of the mood of the market as much as one of facts. The bond hasn't changed, but the market you're selling or buying it in may have.

keshlam
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The prices are never denoted for a fixed period. It's simply what the market trades the bond at at the moment. It seems you don't look at any specific bonds but computed yield curves. Trying to price a single bond with these is convoluted and will never get you the correct price (quoted price). An explanation can be found in this answer.

Yield (yield to maturity) itself is just the interest rate needed to discount the future cashflows to reach the current market price. You can see a detailed example matching Bloomberg here.

Your formula also only works if you look at current yield (which is computed as the bonds coupon rate / price). However, no one really looks at that and your quoted yield curves are definitely in terms of YTM.

AKdemy
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Firstly, you're confusing "current yield", which is always just coupon/price, with the "yield" that you would see for bonds of various maturities. "Current yield" does not mean the yield that you currently get from buying the bond, but a specific term to indicate the yield that you get just from the coupon.

Yield in general has many flavors, and what you see in a "yield curve" with fixed periods is not just based on the coupon, but the price of the bond as well.

To calculate a fair price, most bond investors use some sort of interpolation (via software, of course) between the known terms to come up with a yield for a bond that has an irregular maturity. There's not one interpolation that everyone uses, but there are very common ones that essentially create a smooth curve between nodes.

Now - how to come up with a price for a bond with the interpolated yield curve? It's not as simple. You have to discount every cash flow (coupon payments and final redemption) by the yield on the yield curve that corresponds to the timing of each flow (which usually also fall between the fixed nodes). The sum of those discounted values is the value of the bond.

D Stanley
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