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Time to Maturity for Bond Cash Flows in Discounting

Article Quant Q&A · Author: Jojo
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Summary

The exchange clarifies how term to maturity is used when constructing a discount function from bonds with coupon payments. Rather than assigning one maturity measure to an entire coupon bond, measure the time from the valuation date to each individual cash flow date in years. Each coupon payment and the final principal repayment therefore has its own time to maturity.

For a semiannual coupon bond, the cash flows occur at successive coupon dates, with the final payment at the bond's maturity date. A 30-year bond consequently has 60 scheduled semiannual cash flows, each discounted using the time remaining to that payment. This distinction is useful when setting up discounting or curve bootstrapping. The answer gives the core definition and an example, but does not specify day-count conventions, valuation-date adjustments, or business-day calendar treatment, all of which can affect the precise year fractions used in practice.

Key ideas

  • Term to maturity is the time from the valuation date to a particular cash flow date, expressed in years.
  • A coupon bond has a separate time-to-maturity value for each coupon and principal payment.
  • A 30-year bond with semiannual coupons has 60 scheduled cash flows.
  • Practical year fractions can depend on day-count rules and calendar adjustments.

Tags

Fixed incomeStatistics
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# Term to Maturity when calculating discount function


# Term to Maturity when calculating discount function












I am just trying to understand what TTM (Term to Maturity) means in Page 8 of this PDF when calculating the discount function. Is it just the vector representing the difference between the time to maturity and the various coupon payments for the bonds? For example, if we are considering 1 year, 2 year, 5 year, 10 year and 30 year bonds and each has semi-annual coupons what would the TTM be?

Thank You

## Answer by Helin (score 1, accepted)

https://quant.stackexchange.com/a/19044

It is simply the difference between "today" and the cash flow date in years. A 30-years bond paying semi-annual coupons has 60 cash flows, and each cash flow has its own "TTM".

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.