Pricing Floating-Rate Bonds with Credit Risk and Recovery
Summary
The document explains how to include issuer default risk and recovery when valuing a floating-coupon bond. It points to the Duffie–Singleton framework: discount scheduled coupons and principal using the risk-free discount factor, adjusted for the probability the issuer survives to each payment date. The expected cash flows are then supplemented by the value of recovery payments if default occurs.
The answer notes that accrued coupon is lost upon default and that recovery applies to the remaining principal payments. It describes the resulting dirty price as the value of surviving cash flows plus recovery, with accrued interest subtracted to obtain the clean price. The document gives a conceptual outline rather than a complete formula or implementation. It does not specify how to model default probabilities, recovery timing, or recovery conventions, so those details must be defined for a particular bond and pricing setup.
Key ideas
- Discount each scheduled coupon and principal payment using the risk-free curve and survival probability.
- Include expected recovery value for principal payments when default occurs.
- Accrued coupon is treated as lost in the stated default setup.
- Subtract accrued interest from the dirty price to obtain the clean price.
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# Price of a floating coupon bond with issuer credit risk and recovery rate # Price of a floating coupon bond with issuer credit risk and recovery rate I need help. I have an assignment for an exam where i have to compute the price of a portfolio composed by floating coupon bonds taking into account the issuer credit risk and the recovery rate in case of default. I have to create a code in python. After computed the discount factors, i should price the bonds, but i don't know how to include the issuer risk and the recovery rate in the formula. The professor gave us the interest rates to compute the coupons, and i know that the price of a bonds is given by the sum of the discounted cash flows. How can i insert in the forumula these others two elements? He told me that is a sort of weighted average of the bond's price with the survival probabilitiy and the bond's price in case of default taking into account the recovery rate, with weight survival probability and default probability. But i didn't catch this. Sorry for my basic english and thanks to everyone in advance. ## Answer by Dimitri Vulis (score 1, accepted) https://quant.stackexchange.com/a/65844 It sounds like your professor is asking you to code the formulas in the Duffie-Singleton paper https://web.stanford.edu/~duffie/ds.pdf . (Also found in excellent papers by Bielecki and other sources.) A few technical details to keep in mind: In case of default, bond's accrued coupon is wiped out, and you have recovery only on the remaining principal payments, which you need to price. Discount each cash flow (coupons and principal) by the riskfree discount factor (from your bond financing curve) $\times$ the probability of survival (i.e. 1 - probability of default) at the time of the cash flow. The fair dirty price of the bond is the sum of the above: all the cash flows, plus the value of the recovery in case of default. Subtract the accrued to get the clean price.
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