Pricing Callable Floating-Rate Notes with Hazard-Rate Models
Summary
The document discusses how to value a callable floating-rate note when the issuer’s credit spread changes. Its central idea is that an issuer whose credit quality improves may have an incentive to call and refinance a note that pays a spread above current market levels. This frames the call decision as depending on credit conditions as well as the note’s terms, rather than solely on movements in risk-free rates.
The answer proposes modeling the issuer’s default hazard rate, the instantaneous conditional default probability, with dynamics analogous to a short-rate model. It maps the affine form commonly used for bond prices to a survival-probability function and says the hazard-rate dynamics and parameters must be selected and calibrated. The discussion offers a modeling analogy, not a complete callable FRN valuation framework: it does not specify calibration instruments, call exercise mechanics, recovery assumptions, or how interest-rate and credit risks should be modeled jointly. The spread example motivates the problem but is not evidence that the proposed model is uniquely appropriate.
Key ideas
- An issuer’s improved credit quality can make refinancing a callable floater attractive.
- The response recommends modeling default risk through a time-varying hazard rate.
- An affine survival-probability expression can parallel affine short-rate bond pricing.
- Hazard-rate dynamics and parameters require selection and calibration.
- The answer does not provide a complete valuation or calibration procedure.
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# Pricing Callable Floating Rate Note # Pricing Callable Floating Rate Note I have a question concerning pricing of a callable floating rate note (FRN). I have not found a lot of literature concerning callable FRNs (although a lot for callable bonds). With my understanding, modelling the short rate is no longer relevant here (as would be the case for a callable bond) because interest rate movements do not dictate whether the bond will be called but actually the credit quality of the issuer: ie. if the bond was issued with an issue spread of 100bps (ie. the FRN pays LIBOR+100bps and that 100bps represents the issuer's inferior credit quality over members of the interbank market) but over the course of the life of the bond the issuer's credit quality increases which is revealed in a lower trading spread/par floater spread of say 80bps then, if the strike price of the call was set at par say (ie. 100bps) then the bond would be called. How should one go about modelling the credit quality of the issuer then? Does anybody know of some resources they advise looking at or a better approach to pricing this in general? All help very much appreciated ## Answer by gmarais (score 2) https://quant.stackexchange.com/a/16136 You can resort to a model for the "hazard rate", $\lambda$, where the hazard rate is "the instantaneous conditional default probability". Hull suggests modelling this in exactly the same way you would model the short rate of interest in the Hull-White short rate setup. Recall, for short rates you assume an Affine structure for bond prices $P(t,T)=A(t,T)exp(-r(t)B(t,T))$ The exact same logic applies for hazard rates where instead of a Bond Price $P(t,T)$ you rather have a "Survival Probability" $SP(t,T)$: $SP(t,T)=A(t,T)exp(-\lambda(t)B(t,T))$ In both cases, your job is to select the correct dynamics for $\lambda(t)$ and to calibrate the parameters some how. Hope this help!
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