Mapping Bond Maturities to the Yield Curve in Short-Rate Models

Summary

The document raises a question about using a non-flat term structure when pricing options on bonds with a normal short-rate model. The author describes a proposed mapping for a ten-year bond: at each future point before maturity, use a zero-coupon yield corresponding to the bond’s remaining life. This produces a sequence of yields indexed by remaining maturity, which the author finds counterintuitive compared with listing yields by chronological maturity.

The text contains no answer, derivation, or pricing results, so it does not resolve whether the described input method is correct for the software or model. Its useful contribution is identifying the distinction that needs clarification: a yield curve is commonly organized by the maturity of the zero-coupon instruments, while a bond’s remaining term changes as time passes. Readers would need the model documentation or a worked example to verify how the software expects the curve to be supplied and applied.

Key ideas

• The question concerns relaxing a flat yield-curve assumption when pricing bond options.
• The proposed input maps each future date to a zero-coupon yield for the bond’s remaining maturity.
• Yield curves are commonly represented by yields indexed to instrument maturity, which differs from chronological time passing for one bond.
• The document provides no resolution or evidence confirming the software’s intended convention.

Tags

# A basic question about short-rate models


# A basic question about short-rate models












Sorry, if it's a very rudimentary question. I mainly practice tax but have to deal with financial transactions from time to time where I have to benchmark option prices. I have usually used Hull's Derivagem (normal short-rate model) to calculate option prices on bonds. I have been assuming a flat term structure for simplicity.

However, I'm looking to relax this assumption and use a normal term structure. I have been told that the way term structure goes into Derivagem is as follows. For example, for a 10 year bond: at 1-year maturity, the bond has 9 years remaining until maturity, so we use a 9 year zero-coupon yield; at 2-year maturity, the has 8 years remaining until maturity, so we use a 8 year zero-coupon yield; and so and so forth.

This would give a term structure where yields will down as maturities go up. However, this is a bit counter intuitive to me. I thought we can derive a term structure by listing maturities in a chronological order and then the corresponding zero-coupon yields.

I'd really appreciate if someone could please clarify this concept for me.

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