Interpreting Semiannual Credit Spreads from Rating Transitions

Summary

The document poses a credit-risk question using a three-state annual transition matrix for ratings A, B, and default. It asks for the credit spread ten years ahead for a company currently rated B, with the spread calculated semiannually. The author understands a spread as the negative logarithm of solvency and suggests raising the annual transition matrix to the ten-year horizon to obtain default probability and survival probability.

The uncertainty is how the semiannual convention changes that calculation: whether it calls for a half-year transition step as well as a ten-year horizon, or for converting a ten-year survival probability into a semiannual rate. The document provides no answer, calculation, or convention-specific evidence, so it is best read as a statement of the problem rather than a method. It also does not specify recovery assumptions or whether the requested spread is a continuously compounded or periodically quoted rate, details that can affect interpretation.

Key ideas

• The setup gives annual transition probabilities among two credit ratings and default.
• The requested quantity is a spread for a B-rated company at a future horizon, quoted semiannually.
• The author proposes using the transition matrix to obtain future default and survival probabilities.
• The document leaves unresolved how the semiannual convention applies to the horizon and spread conversion.
• Recovery assumptions and the spread quotation convention are not specified.

Tags

# Credit Spread, Transition Matrix


# Credit Spread, Transition Matrix












Consider a credit rating system consisting of three credit states, A, B and D (default) with the following annual credit transition probability: T = [0.7 0.2 0.1;0.2 0.5 0.3; 0 0 1].

For a company rated B, calculate: a) The credit spread, calculated semi-annually, ten years into the future.

The semi-annually is throwing me off. I know that credit spread = - ln q where q is the solvency. For ten years into the future, we simply take T^10 and the solvency is just 1-default. But they want the credit spread calculated semiannually, ten years into the future.

Edit: I'm wondering if it's asking two different questions ie. calculate credit spread semiannually (T^1/2) and ten years into the future (T^10), or is there a way to calculate the semi annual rate ten years into the future?

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