Interpreting Bankruptcy Frequencies in ALM Monte Carlo Simulations

Summary

The document asks whether the fraction of simulated asset-liability management paths ending in bankruptcy can be read as the real-world probability of bankruptcy. Its answer cautions that a simulation percentage is not an exact probability estimate simply because many paths were generated. The result depends on whether the model’s assumptions reflect the real world, and those assumptions will generally not hold exactly.

When the assumptions are approximately valid and the simulation includes enough paths, the share of paths ending in bankruptcy may provide an approximate indication of risk. The simulations can also help illustrate possible future outcomes. The discussion is qualitative: it gives no method for choosing assumptions, quantifying model error, or determining how many paths are sufficient, so the frequency should be interpreted as conditional on the model rather than as a definitive real-world probability.

Key ideas

• A simulated bankruptcy frequency is not automatically the real-world bankruptcy probability.
• The estimate depends on how closely the simulation assumptions match reality.
• With reasonably appropriate assumptions and enough paths, the frequency can offer an approximate risk indication.
• Monte Carlo paths illustrate possible outcomes but do not guarantee a precise forecast.

Tags

# Asset Liability Management, probabilty of realising the paths in a Monte Carlo simulation


# Asset Liability Management, probabilty of realising the paths in a Monte Carlo simulation












An ALM study produces several future real world interest paths, lets say the set consists of 5000 of such paths. What is the chance that one such path becomes reality? If in 50% of the paths the company goes bankrupt can we conclude that the probably of bankruptcy is 50%?

## Answer by Bob Jansen (score 1, accepted)

https://quant.stackexchange.com/a/31556

No, you can't.

In general, these paths are created using assumptions that will not exactly hold in the real world and therefore the outcome of the simulation will never be an exact estimate of the real probability, independent of the number of simulations you use.

However, if the assumptions approximately hold and you create a sufficient amount of paths the percentage of paths end up in bankruptcy would hopefully come close to the real probability. At the very least they should give you some idea what the future might bring.

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