bonds – relevant across FI models #HJM..

Bonds are no longer the dominant FI instrument, challenged by IRS and futures. However, I feel for Fixed Income models bonds are more important, more useful than any other instrument.

– Bond (unlike swap rates, FRA rates etc) is a tradeable, and obeys many nice martingale pricing rules.

– Zero Bond can be a numeraire.

– For model calibration, zero bond prices are, IMO, more easily observable than swap rates, FRA rates, cap prices, swaption prices etc. I think futures prices could be more “observable” but the maturities available are limited.

– Zero bond’s price is exactly the discount factor, extremely useful in the math. I believe a full stochastic model built with zero bond prices can recover fwd rates, spot rates, short rates, swap rates and all others …

– I believe term structure models could be based on fwd rate or short rate, but they all need to provide an expression for the “zero bond process” i.e. the process that a given bond’s price follows. Note this process must converge to par at maturity.

– Bond as an instrument is closely related to caps and floors and callable bonds.

– Bonds are issued by all types of issuers. Other instruments (like swaps, IR futures) tend to have a smaller scope.

– Bonds are liquid over most regions of the yield curve, except the extreme short end.


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