# How to model potential exposure, post-Archegos

## BofA quant’s model considers the correlation between market shocks and counterparty defaults

As modelling errors go, Credit Suisse’s miscalculation of its credit exposure to Archegos Capital Management might take the biscuit. The bank estimated its potential exposure at around $550 million just days before suffering a$5.5 billion loss.

Archegos was an extreme case, but forecasting errors of this type are all too common. In recent years, the defaults of several highly levered investors – including hedge fund Malachite Capital Management and commodity trader Einar Aas – have left banks and central counterparties with surprisingly large losses.

Andrew Dickinson, a director in the quant strategy and data group at Bank of America, argues the standard approaches used by banks to model their exposure to levered counterparties fail to adequately capture the correlation between market jumps – the sort of violent price moves that generate chunky margin calls – and the probability of default.

“Classical models like conditionally independent default models may link the chances of a counterparty default with what happens in the market, but they do so in a milder fashion”, he says. “They don’t fully capture the sort of coalescence of adverse events when it comes to both extreme gaps in the market and the counterparty defaulting on the same day.”

Approaches such as jump-to-default models don’t explicitly tie the probability of default to market gaps. Dickinson’s latest paper describes a model for calculating potential exposure – a common measure of counterparty risk that provides a reasonable estimate of worst-case losses in a default – that takes this correlation into account.

“The model needs to capture the possibility of jumps – not just normal jumps, but also fat-tail jumps – and the chances of a material jump occurring needs to be realistic,” he says. “Then it needs to capture meaningfully the possibility of counterparties defaulting due to the variation margin call.”

###### The model needs to capture the possibility of jumps – not just normal jumps, but also fat-tail jumps – and the chances of a material jump occurring needs to be realistic

Andrew Dickinson, Bank of America

The latter piece brings up the thorny question of wrong-way risk. “The counterparty may be using some of their assets as collateral – as protection against default,” notes Chris Kenyon, head of quant innovation and derivatives valuation adjustment (XVA) modelling at MUFG. In such cases, when the assets decline in value, the bank is more exposed and less protected.

Dickinson uses orthodox inputs – probability of default, recovery rate and expected exposure – to model these dynamics. He then uses a t-distribution to capture fat tails and Lévy processes to replicate market gaps. But the key ingredient that distinguishes this model from classical approaches is the introduction of a correlation parameter that links market gaps to default intensity. The parameter ranges from zero to one – when it equals zero, the model reduces to a classical form, but as it moves towards one, the model signals an increasing frequency of market gaps and coincident defaults.

When the correlation parameter is close to one, a severe but plausible decline in the value of a counterparty’s portfolio is likely to trigger a default. In such scenarios, banks should limit exposures and ensure they have collected enough initial margin to absorb losses.

“If a counterparty has 1 billion dollars of liquid capital, a broker-dealer should make sure their portfolio is limited in size so that the counterparty would lose at most 1 billion dollars over initial margin under a severe but plausible scenario,” says Dickinson.

If the model is widely adopted, highly levered counterparties would have to demonstrate that they are sufficiently capitalised to withstand a severe but plausible market gap in order to do business with banks. It is hard to see how Archegos could have passed that test in the months and weeks leading up to its collapse.

That, of course, assumes that banks are able to get reliable data on counterparty positions – as Archegos’s counterparties rapidly discovered in the advent of the fund’s demise.

“The limiting factor is actually knowing what assets your counterparty has,” says Kenyon. The model provides useful and reliable information, he says, “only if you could have gotten the calibration data”.

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