merton.portfolio.concentration

Concentration metrics.

Functions

hhi(→ float)	Herfindahl-Hirschman Index of a portfolio.
effective_n(→ float)	Effective number of names 1/HHI.
granularity_adjustment(→ float)	Pykhtin-Dev (2002) granularity adjustment for the IRB asymptotic VaR.

Module Contents

merton.portfolio.concentration.hhi(exposures: merton._typing.ArrayLike) → float

Herfindahl-Hirschman Index of a portfolio.

\[\mathrm{HHI} = \sum_i w_i^2,\quad w_i = \frac{E_i}{\sum_j E_j}.\]

Ranges in [1/n, 1]. A perfectly diversified portfolio of n equal exposures has HHI = 1/n; a portfolio concentrated in one name has HHI = 1.

merton.portfolio.concentration.effective_n(exposures: merton._typing.ArrayLike) → float

Effective number of names 1/HHI.

merton.portfolio.concentration.granularity_adjustment(pd: merton._typing.ArrayLike, lgd: merton._typing.ArrayLike, rho: merton._typing.ArrayLike, exposures: merton._typing.ArrayLike, *, alpha: float = 0.999) → float

Pykhtin-Dev (2002) granularity adjustment for the IRB asymptotic VaR.

Computes the leading-order correction to the Vasicek IRB VaR for finite portfolio size. Returns the additive adjustment in units of exposure fraction (so the actual VaR upper bound is VaR_IRB(pd, lgd, rho) + granularity_adjustment(...)).

Pykhtin & Dev (2002) Credit Risk in Asset Securitizations. Risk 15(5).