"Gambling on Monte Carlo simulations
A mathematical model developed by physicists working on the atomic bomb in the 1940s and named after a gambling hub, is probably a fitting one for the US government to adopt in its banking stress tests.
While Friday’s release of the methodology for the tests contained little new on the loan loss assumptions of the exercise (the assumptions about GDP, unemployment and house prices had already been published) there was this bit from the paper:
Analysis of [commercial and industrial] loan loss projections was based on the distribution of exposures by industry and by internal rating provided by the firms. In many cases, these ratings were mapped to default probabilities by the firm; in other cases, this association was established by supervisory analysts. This information was confirmed and supplemented by external measures of risk, such as expected default frequencies from third party vendors. Supervisors evaluated firm loss estimates using a Monte Carlo simulation that projected a distribution of losses by examining otential dispersion around central probabilities of default. The approach produced a consistently‐prepared set of loss estimations across all the BHCs by combining firm‐specific exposure and rating information with standardized assumptions of the performance of similar exposures. The results of this analysis were compared to the firms’ submissions and adjustments made to ensure consistency across BHCs.
Monte Carlo simulations are pretty standard things in finance. They’re used to value not just potential loan losses but also portfolio risk and derivatives.
While there’s no single Monte Carlo method they tend to work like this: Define a domain of possible inputs, generate inputs randomly from the domain, apply some algorithms, then aggregate the results. In playground terms, you can imagine it as a game of battleship. First a player makes some random shots on their opponent’s board. Then they apply the maths (in this case, a battleship is a vertical or horizontal line of four or five dots) and then determine the likely locations of their opponent’s ships.
The good thing about Monte Carlo simulations is that they do well modelling things with lots of uncertainty and complexity in inputs. However, as the above should have suggested, they’re very much limited by their range of actual inputs. This snippet, from a May 2007 Bloomberg article on CDOs and subprime is a perfect illustration.
Because there are so many moving parts to a CDO, rating companies have to assess not only the chance that something may go wrong with one piece but also the possibility that multiple combinations of things could falter. To do that, S&P, Moody’s and Fitch use a mathematical technique called Monte Carlo simulation, named after the Mediterranean gambling city.
The rating companies take all the data they have on a CDO, such as information about specific bonds and securitizations and the remaining types of loans to be purchased for the package.
The firm enters data into a software program, which calculates the probability that a CDO’s assets will default in hypothetical situations of financial and commercial stress. The program effectively rolls the dice more than 100,000 times by running the information randomly.
If the inputs and assumptions are wrong then the Monte Carlo simulations will be of very little use. In that sense they’re very similar to the magic worked by David Li’s Gaussian Copula. They give a false sense of security.
And that’s precisely, some might argue, what the US government is going for with its bank stress tests anyway.
Related links:
Of couples and copulas - Sam Jones, FT
Dual stance on valuing bank securities - FT
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