Implied Forward Rates from Zero-Coupon Bond Spot Rates

Summary

The document poses a fixed-income question: how to lock in a one-year rate that begins three years from now using zero-coupon bonds with maturities from one to four years. It supplies annually compounded spot rates for each maturity and asks which bonds to combine and what forward rate that implies.

The response identifies the target as the forward rate between years three and four, but does not show the bond positions or calculate the rate. Instead, it points the reader toward the relationship between spot and forward rates and encourages working through it. As a result, the prompt offers a useful exercise in extracting a forward rate from a spot curve, while providing no worked derivation, numerical answer, or discussion of assumptions beyond annual compounding and the stated rates.

Key ideas

• A one-year rate starting in three years is the forward rate for the interval from year three to year four.
• The relevant spot rates are those for maturities that span the deferred investment period.
• The prompt asks for a bond combination but does not provide the solution.
• The question assumes annual compounding and the given spot rates.

Tags

# Zero coupon bonds


# Zero coupon bonds












Assume the zero-coupon bonds from 1 year to 4 years are all available, and the current 1-year, 2-year, 3-year and 4-year spot rates are 4%, 5%, 6% and 7% accordingly. Interest rates are annually compounded. You want to lock in a 1-year interest rate beginning in 3 years, by using some of the zero-coupon bonds above.

Question: ) Which zero-coupon bonds would you use?

And what is the locked-in 1-year rate beginning in 3 years?

## Answer by SmallChess (score 0, accepted)

https://quant.stackexchange.com/a/17939

You're asking for the forward rates between 3y and 4y. I don't want to tell you the answer because it's something that you should attempt. Please read the section on forward rates and how to get the implied interest rate from a zero coupon bond.

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.