Wrong-way risk, or the risk of a firm's exposure being highly correlated to the default of the associated counterparty, has never been easy to model. It is typically captured as a correlation between credit spreads and the market risk factors that drive exposure, but often banks turn a blind eye to it. "In general, banks don't care about the issue," notes Dariusz Gatarek, a professor of finance at the Polish Academy of Sciences in Warsaw. "In most cases they say the correlation is very low, and ignore it."
There are a number of reasons for this. First, correlated counterparty defaults happen rarely – although when they do, they can produce large shocks, especially when a bank's defaulting counterparty is systemically important. Second, existing methods are unintuitive. As a result, dealers typically have systems and pricers, or tools used to price specific derivatives contracts, that are based on the assumption that credit and market risk factors are independent.
There are two main types of models currently being considered by dealers: stochastic default intensities and copula models. The former models the probability of the default of a counterparty at a given point in time as a random stochastic process and correlates it with risk factors. The latter is modelled as a joint distribution of default and risk factors, which in turn helps look at the dependence between these variables. However, both have major drawbacks.
Stochastic default intensities create a lot of complexity, some argue, without a corresponding improvement in accuracy. "They can be hard to calibrate and they are harder to simulate and implement. On top of this, they do not create enough correlation between a credit event and a market risk factor, and sometimes produce results conflicting with expectations," says Fabio Mercurio, head of quantitative analytics at New York-based information vendor Bloomberg. "For copula methods, on the other hand, you are not correlating variables in an intuitive manner, and you don't know what the correlation parameter really means."
In our first technical paper, Jumping with default: wrong-way risk modelling for CVA, Mercurio and colleague Minqiang Li, a quantitative analyst in his team, offer easy approximation techniques for wrong-way risk, which they claim would overcome these drawbacks.
Mercurio and Li add a jump process to market risk factors in their credit valuation adjustment (CVA) calculations. They say this offers a more intuitive way of looking at how exposures would move in the event of a counterparty default, since they capture the effect using a single jump parameter. "The simplicity of the results is such that you can actually summarise the correction to CVA in a single parameter. So our jump size can be quoted like an implied volatility, where instead of stating the price of the option, you can state the implied volatility," explains Mercurio.
Many banks already apply such jumps to emerging market exposures, but don't necessarily apply them more broadly across instruments such as foreign exchange and interest rate derivatives. The pair's general framework applies to both and they claim that fairly straightforward modifications can be made to existing pricers to implement the framework for specific asset classes. For example, for a portfolio of plain vanilla forex derivatives, banks only need to change the value of the initial exchange rate input. In the case of plain vanilla interest rate derivatives, only the relevant pricing curve needs to be shifted.
In our second paper, FVA for general instruments, Alexandre Antonov, a senior vice-president in the quantitative research team at New York-based software vendor Numerix, Marco Bianchetti, a senior quant and risk manager in the market risk management department of Italian bank Intesa Sanpaolo, and Ion Mihai, a director of financial engineering at Numerix, propose an approximation method for calculating the funding valuation adjustment of portfolios of both vanilla and exotic derivatives.
Risk.net launches Cutting Edge Investments
Every month this new section will publish peer-reviewed papers on topics relevant to the buy side, such as portfolio management, risk control, trading strategies and algorithmic trading.
We encourage quants from hedge funds, asset management firms and pension funds to submit their research papers to Risk for review, using the email address [email protected]. Submission guidelines can be found here.
In the first paper of this series, Attilio Meucci, Alberto Santangelo and Romain Deguest introduce the concept of so-called minimum-torsion bets and explain how it can be applied to portfolio diversification. Minimum-torsion bets are a set of uncorrelated risk factors that have intuitive interpretation because they closely resemble commonly used risk factors. This differentiates them from the well-known principal components analysis method, which often identifies factors with no obvious financial meaning. They devise a novel approach to risk budgeting and risk parity that allows the risk manager to control risk contributions effectively.