Credit Migration Matrix Simulator

Why Default Probability Only Ever Rises

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The Shape Of The Migration Path

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Why This Matters For Portfolio Risk

A bond portfolio manager holding a diversified pool of A and BBB credits isn\u2019t just exposed to today\u2019s default rate, they\u2019re exposed to the whole migration path, since a downgrade well before default already destroys mark-to-market value through wider credit spreads. This model makes that full path visible rather than collapsing it to a single one-year default statistic.

The Core Formula

π_t is the row-vector rating distribution at time t, and P is the transition matrix where each row is a valid probability distribution summing to 1. Default is modeled as an absorbing state, once entered, it is never left.

When To Actually Use This Model

• Projecting a bond or loan portfolio's expected rating migration and cumulative default probability over a multi-year horizon.
• Teaching Markov chain applications in credit risk and fixed income courses.
• Stress-testing how sensitive long-run default rates are to specific transition probabilities, particularly the lowest-rated tier's default rate.
• Building the underlying engine for a ratings-based economic capital or provisioning model.

Key Assumptions & Limitations

• Assumes the transition matrix is constant (time-homogeneous) over the full horizon; real transition probabilities vary with the credit cycle.
• Assumes the Markov property, next year's transition depends only on today's rating, not on how the firm got there or how long it's been at that rating.
• This simplified four-state matrix collapses the much finer-grained rating scales agencies actually use (typically 10+ notches).
• Real rating agencies publish empirically estimated matrices that vary meaningfully by industry, region, and time period.

Foundational Reference

Jarrow, R. A., Lando, D., & Turnbull, S. M. (1997). A Markov Model for the Term Structure of Credit Risk Spreads. The Review of Financial Studies, 10(2), 481-523.