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I'm trying to wrap my head around bonds.

There are many types of bonds, but to put it simply, it can either be floating rate or fixed rate, and it can also have collateral to account for the credit risk (like ABS bonds).

Now, it seems to me that ALL we need to understand everything there is to understand about bonds, is two things:

  1. The discount curve: the cash flows of the bonds will be discounted using this discount curve, so that we can get the present value.
  2. The fixing curve: this is only needed if the bond is floating rate. It is used to actually calculate the above cash flows (approximately, ie using expected future rates, since we dont know whats actually realized)...and then we discount as before.

My confusion is this: how do you actually determine these curves? How do I know what discount and fixing curve to use? Are they specified in the literal contract? Or do you pick them randomly yourself? And how does the choice depend on whether the bond is fixing or float, and how do we adjust for higher credit risk, and what happens if the bond also has collateral (like mortgage-backed securities) and what happens as that collateral is diminished as time goes by (e.g. if you have a mortgage backed security, what happens if as time goes by, some mortgage payers default and so the collateral becomes worth less?)

I think the fixing curve must be specified in the contract so if thats the case, all my questions for that are answered: but what about the discount curve?

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The choice of discount curve is not an exact science. It should incorporate the risk of default of the issuer and the future expectation of interest rates. It's certainly not specified in the contract.

There are various methods of determining a discount curve for a given bond. One method it to look at other bonds from the same issuer and see what yields they are trading at, then inferring risks of default (or just bootstrapping/interpolating discount rates) to find rates to use for discounting. A more simplistic method is to use curves based on the credit rating of the bond (or issuer) or for broader curves at the sector on industry level.

None of this derived data is publicly available - data providers charge a premium for access to this curve data since it's not trivial to calculate. It's also not precise. The discount rate for a bond can vary significantly between the bonds from the same issuer, so you may over- or under-price an individual bond if you don't use the right discount curve.

For a floating-rate note, you typically use a different discount curve than the reference curve that's specified in the contract (otherwise you are assuming virtually no default risk) but the process is the same since an issuer has the same risk of default whether they issue a fixed- or floating-rate bond. If you look at the discount curve as a combination of the fixing curve plus some level of credit risk, then you effectively "cancel out" the underlying fixing rate and are just exposed to the default risk.

As a side note, while ABS does have "collateral" that reduces the risk of default, there is prepayment risk that investors look at to see if they'll get their investment back sooner than they had anticipated. Some ABS investors want to lock in the expected payment rate for a longer period of time, so they don't want it to be paid off early.

Put simply, ABSs are structurally similar to bonds but have very different drivers and risks.

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