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Modelling Default Risk in the Trading Book: Accurate Allocation of Incremental Default Risk Charge Jan KwiatkowskiPowerPoint Presentation

Modelling Default Risk in the Trading Book: Accurate Allocation of Incremental Default Risk Charge Jan Kwiatkowski

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Modelling Default Risk in the Trading Book: Accurate Allocation of Incremental Default Risk Charge Jan Kwiatkowski

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Modelling Default Risk in the Trading Book: Accurate Allocation of Incremental Default Risk ChargeJan Kwiatkowski

Group Risk Management

- Background on IDRC
- Trading book default risk models
- The need for accurate allocation
- Andersen, Sidenius & Basu (ASB) algorithm
- Conditional Expected Loss; an allocation metric
- Calculation using Bayes’ Theorem
- Extensions

- Required to find high percentile of portfolio default losses over a given time horizon.
- We prefer Conditional Expected Shortfall (CES) at equivalent percentile:
- The book tends to be ‘lumpy’; therefore we must include idiosyncratic effects.

- Many models use systematic risk factors and correlations

- Require an algorithm for computing distribution of portfolio loss conditional on any X
- Integrate over X (e.g. Monte Carlo or quadrature)

- Monte Carlo
- Transforms
- ASB
- Must keep in mind the need for allocation

- Total IDRC is allocated/attributed to contributors (down to position level), and aggregated up the organisational hierarchy.
- Allocation must be ‘fair’ and consistent
- Especially, desks with identical positions should get the same allocation.
- Using Monte Carlo for high percentiles , we are at the mercy of relatively few random numbers
- Transforms not convenient for allocation

Discretise LGD’s as multiples of a fixed ‘Loss Unit’

ui= loss units for issuer i

Let qi= PD for issuer i (conditional on givenX )

Recursively compute the distribution of the losses for portfolios consisting of the first i exposures only, for i =0, 1, 2, …., N

- The method is exact modulo discretisation
- Parcell (2006) shows how effects of discretisation may be mitigated
- Easily extended to multiple outcomes

Exactly accounts for portfolio CES

- We can easily calculate this by removing issuer i fromthe final portfolio and adding its LGD, ui, to the resulting portfolio distribution.
- We use the reversal of the ASB algorithm to remove issuer i

We illustrate this for a long position (ui>0); this is easily adaptable to short positions.

- This becomes unstable forqi>0 close to 1.
- Can be mitigated (Parcell 2006)

- For various systematic effects, X, use ASB to find the conditional distribution.
- Integrate over X
- Compute Lα, the required portfolio CES

- For each issuer, i:
- for each X
- Use reverse ASB to find the distribution with i defaulted.
- Compute the corresponding probability that Lα is exceeded
- Multiply by uiqi/(1-α)

- for each X
- Integrate over X

- The method for VaR (rather than CES) is even simpler
- Multiple outcomes:
- Stochastic LGDs
- Rating Downgrades
- Also upgrades, but requires matrix inversion

- Structured products – cascade structure