Applying the Basel–Vasicek Capital Formula Across Multiple Years

Summary

The document asks whether the Basel–Vasicek unexpected-loss formula can be applied over a 20-year horizon, both to cumulative risk and to each year separately. It presents the formula in terms of loss given default, probability of default, asset correlation, and a high confidence quantile, and questions whether its derivation assumes a one-year horizon.

The text raises a useful modeling issue but does not provide an answer or establish how the formula should be adjusted. It gives no evidence, numerical example, or method for combining annual default risk into a multi-year measure. Readers should therefore treat it as an open question rather than guidance for calculating long-horizon capital. Resolving it would require specifying the default-time model, how probabilities and exposures evolve, and whether the desired quantity is cumulative loss or annual capital; those distinctions are not addressed here.

Key ideas

• The document asks whether the Basel–Vasicek unexpected-loss formula can represent risk over a 20-year horizon.
• It distinguishes cumulative horizon risk from a year-by-year capital calculation.
• It questions whether the formula's derivation depends on a one-year horizon.
• No answer or worked method is supplied, so the question remains unresolved in the text.

Tags

# Multi-period Basel/Vasicek formula


# Multi-period Basel/Vasicek formula












I need to apply Basel/Vasicek formula to a 20-years horizon, both from a 20-years cumulative perspective and year-on-year basis.

Please find below the formula of the Basel Capital (ie. unexpected loss):

$$ {\displaystyle K=LGD*\left[N\left({\sqrt {\frac {1}{1-R}}}*G(PD)+{\sqrt {\frac {R}{1-R}}}*G(0.999)\right)-PD\right]} $$

From my understanding there is no issue in it: this limiting formula was derived with no assumption on 1-year horizon.

Am I misunderstand anything? What?

Gratefully.

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