Default-Adjusted Cash Flow Valuation for Floating-Rate Bonds
Summary
The document discusses how credit risk changes the valuation of a floating-rate corporate bond. A risk-free floating-rate valuation may project coupons using forward rates and discount them on a reference curve, but a risky issuer introduces default and recovery effects that must also be represented. The answer points out that risky floating coupons may include a credit spread over the reference rate, and suggests an approach analogous to credit default swap valuation.
Under the stated framework, each cash flow is discounted using a funding-based discount factor and adjusted for the chance the issuer survives to the payment date. A separate default component accounts for the probability of default during the period, recovery, and remaining principal. The document assumes default probabilities and a recovery convention are available, and briefly describes coupon cancellation and accelerated principal repayment following default. It does not specify how to estimate those inputs, calibrate a curve, or handle market-specific conventions, so it is an outline rather than a complete pricing recipe.
Key ideas
- A risky floating-rate bond may pay a spread over its reference rate.
- Credit risk affects both coupon and principal cash flows.
- Expected cash flows can be adjusted for survival and default probabilities, with recovery included after default.
- Discounting and recovery assumptions are needed to value the bond.
- The answer gives a conceptual framework but not a method for estimating its inputs.
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# Valuation of Floating Rate bond # Valuation of Floating Rate bond Let say, I have some `floating rate bond` where the coupon depends on `6-month Libor` with semi-annual payments. In a typical text-book, the way this bond is priced (dirty-price) is that, replace `expected future Libor rate` as `Forward 6-month Libor rates` and then discount those cash-flows with `Libor` rate again, using same Libor term-structure as seen today. I feel this makes sense based on the `T-forward measure`. Now let say, this Bond is `Corporate bond`. In this case, how does it make sense to discount it using `Libor`? Should not we use different `term-structure of Yield` based on the `Credit-Rating`? But in that case, how to mathematical basis of using `T-forward measure` would still hold? Or, we should still use the `Libor` as discounting and then make `Credit-value adjustment` after I get the risk-free pricing using Libor? In that case, how should I calculate the `Credit-value adjustment` for this case? Really appreciate for any help to understand the mathematical basis for risky floating rate bond pricing. ## Answer by Dimitri Vulis (score 2) https://quant.stackexchange.com/a/59319 If a floating coupon bond is risky, then for one thing the coupon is probably not flat libor, but rather libor + some spread. (In some markets they use gearing here, but that has other problems.) To take into account the riskiness of the bond (fixd or floating coupon, does not matter), you can take an approach similar to pricing a credit default swap. It is described in more detail in Thomas Bielecki's paper as well as in Duffie, Singleton Modeling Term Structure of Defaultable Bonds. Suppose that you know the probability of default at each point in time, and the recovery assumption (what the bond will be worth after default). The way bankrupcy laws work in most civilized countries, if a bond defaults, then the accrued coupon is wiped out, and any remaining principal is accelerated and payable immediately. The mark to market of each of the bond's cash flows is: discount factor based on the cost of funding, times: the cash flow amount (interest (doesn't matter whether the bond pays fixed or floating coupon) and principal) times (1 - default probability on cash flow date) plus the probability of default provided there was no default until period start times recovery times remaining principal
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