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101 Concepts for the Level I Exam

Essential Concept 71: Value of a Bond and its Credit Spread, Given Assumptions about the Credit Risk Parameters

For credit analysis of a risky bond in a volatile interest rate environment, we use the arbitrage-free framework.

The first step in the arbitrage-free framework is to build the binomial interest rate tree under assumption of no arbitrage. Once the tree is built we need to verify that it is correctly calibrated.

Analyzing a fixed-coupon corporate bond:

This tree can then be used to analyze a fixed-coupon corporate bond. The steps are:

  1. Determine value of bond assuming no default (VND)
  2. Calculate credit valuation adjustment (CVA)
  3. Fair value of bond = VND – CVA
  4. Using fair value determine YTM.
  5. Using YTM determine credit spread.

Analyzing a floater:

We can also use the arbitrage-free framework to analyze a floater. The process is similar to the analyzing a fixed coupon security. The steps are:

  1. Calculate the VND given the quoted margin (QM)
  2. Calculate the CVA
  3. Fair value = VND – CVA
  4. Use trial and error to determine the discount margin (DM).

Impact of change in interest rate volatility: A change in the assumed level of interest rate volatility has a small impact on the fair value of a corporate bond.