Pricing a Credit-Risky Zero-Coupon Bond on a Short-Rate Lattice

Summary

The document presents an exercise in valuing a zero-coupon bond with default risk using a binomial short-rate lattice. The setup specifies an initial short rate, up and down factors, equal branch probabilities, and a node-dependent one-step hazard rate. The bond has a stated face value and recovery fraction. The central question is how to combine the interest-rate lattice, default probabilities, and recovery in a backward pricing calculation.

No pricing recursion or numerical bond value is supplied, so the document serves as a problem statement rather than a worked method. To obtain a well-defined price, an implementation would need to specify precisely when default is assessed, how recovery is paid, and how the hazard rate is interpreted over each step. It also does not discuss calibration, risk-neutral assumptions, or dependence between rates and default risk, which can affect a practical valuation.

Key ideas

• The exercise combines a binomial short-rate lattice with node-specific default hazard rates.
• A risky zero-coupon bond valuation must account for both survival payments and recovery upon default.
• The document asks for a lattice pricing method but gives no recursion or computed price.
• Default timing, recovery timing, and risk-neutral assumptions are not specified in the prompt.

Tags

# How to price a credit-risky zero-coupon bond?


# How to price a credit-risky zero-coupon bond?












I recently received the following exercise:

> Construct a $n=10$-period binomial model for the short-rate, $r_{i,j}$. The lattice parameters are: $r_{0,0}=5\%$, $u=1.1$, $d=0.9$ and; $q=1−q=1/2$.

This I did do at this point without any problems.

> Assume that the 1-step hazard rate in node $(i,j)$ is given by $H_{i,j}=ab^{j-i/2}$ where $a=0.01$ and $b=1.01$. Compute the price of a zero-coupon bond with face value $F=100$ and recovery $R=20%$.

Now this is a novel part for me as I till now did not price zero-coupon bonds with a default risk.

My question from here is how do I, incorporate the values of the hazard lattice as well as the recovery rate into a zero-coupon bond pricing lattice. (Thus what formula would I use in order to do so correctly)?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.