Extreme Monte Carlo Rate Paths and Mortgage Risk Metrics

Summary

The document considers whether to constrain Monte Carlo interest-rate paths when a calibrated model produces unusually high forward rates. The model described calibrates log-normal skew and mean reversion monthly to a basket of at-the-money swaptions and caps. The question links those extremes to valuation measures such as option-adjusted spread and effective duration for mortgage-related assets.

The response cautions that removing paths changes the expectation of bond prices and can therefore break the fit to market prices. It suggests that low-probability extreme paths may have limited influence on expectation-based measures, including OAS and effective duration. This is a brief qualitative answer: it does not quantify the effect, prescribe a definition of a reasonable path range, or show a sensitivity analysis. The impact depends on the calibrated distribution and the valuation setup, so the claim about limited influence is not established as a general result.

Key ideas

• The question concerns extreme forward-rate outcomes in calibrated interest-rate Monte Carlo simulations.
• The described calibration uses swaptions and caps to fit log-normal skew and mean reversion.
• Removing simulated paths can change expected bond prices and impair market-price fit.
• The response argues that low-probability extremes may have limited influence on expectation-based measures, but supplies no quantitative test.

Tags

# Should we apply practical constraints on the distribution of monte carlo paths?


# Should we apply practical constraints on the distribution of monte carlo paths?












to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out caps. Sometimes resulting in at least five percent of the paths exceeding 40% (1 month forward rate) and reaching over 250%. Most / many months - the highest paths never exceed 50%. Also - any recommendations on how to analyze how this affects resulting metrics such as OAS or effective duration for mortgage-related assets?

## Answer by adam (score 2)

https://quant.stackexchange.com/a/2838

If you start removing some of the paths, then the expectation of the bond prices that you calculate will not fit the market prices. Since these paths are on the extremes, they should not be affecting your OAS or effective duration much (the probability on these paths are low, and all these statistics depend on the expectation).

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