For Martin, the story begins in 1992, when he graduated from Cambridge University with a degree in mathematics and started work in the research division of UK telecom infrastructure company GEC (now known as Marconi). Martin recalls: “I was trying to model failures in large telecommunications systems. Each time a failure occurred in the system, there was a cost associated with it. GEC wanted me to look at worst-case scenarios, at very high confidence levels, and it was then that I realised the applicability of saddle point methods, which I had studied at Cambridge.”
Meanwhile, completing a part-time PhD in time-series modelling at University College London, Martin became aware of opportunities in finance. In early 1998, he attended a job interview at (pre-merger) Paribas. Martin comments: “There was discussion of Raroc, which was then becoming a hot topic. I realised the saddle point method could be applied to problems in credit portfolios.” Martin got the job, and in December 1998, his idea first appeared in Risk, in a paper co-authored with Angelo Arvanitis, Jon Gregory and Christopher Browne.
By summer 2000, after various personnel and management changes at the firm, Browne set up the BNP Paribas fixed-income capital management team. After publishing a short paper on the term structure of credit spreads in January 2001, the team – consisting of Martin, Browne (now at Credit Suisse First Boston) and Kevin Thompson – submitted the series of papers that would contain Martin’s key insights.
The first of these papers, ‘Taking to the Saddle’, published in June, expanded on the 1998 paper. The method works by using a Fourier-transformed variant of the portfolio loss distribution – the moment generating function (MGF). It turns out that the stationary points of the MGF – which can be imagined as the flat areas (or saddle points) of a mountain range – contain lots of information about the shape of the loss distribution. This is important, because the portfolio loss distribution is notoriously hard to work with, particularly in the tail portion corresponding to large unexpected losses in a bank. However, the saddle points of the MGF are much easier to find, and by exploring the shape of the MGF near these points, vital information such as the shape of the tail of the loss distribution can be obtained without costly Monte Carlo simulation. Moreover, this method works best for large, complex portfolios, and is an improvement over other techniques, such as extreme value theory.
In the 1998 paper, Martin applied the saddle point method only to portfolios with independent defaults. Today, the most pressing issue facing the industry is the problem of non-independent or correlated defaults in credit portfolios. Here, the problems of simulating the portfolio loss distribution become immense, but yet again, Martin’s analytic approach pays dividends.
In classical statistics, correlation appears as an objective parameter that can be extracted from pairs of time series, then used predictively to relate one probability distribution to another (such as stock price returns). In credit portfolio modelling, there is often insufficient data on defaults or ratings changes to reliably obtain such a parameter.
The various credit portfolio models that appear subsumed within the Basel II internal ratings-based approach get round this problem by postulating a systematic risk factor or ‘hidden variable’, which behaves like a correlation parameter. This parameter cannot be observed directly, but if it is specified, the loss distributions of individual assets in a portfolio can be treated as being independent. Although he was not the first to notice how the various credit portfolio models in existence had this property in common, Martin has usefully recast the insight in the formalism of non-classical, Bayesian statistics.
According to Martin, hidden variable approaches to credit risk are a version of so-called Bayesian networks or graphical models, a framework whereby observed, conditionally dependent events are depicted as nodes independent of each other, but collectively dependent on one or more hidden nodes. Lines connecting nodes correspond to conditional probabilities. As one expects in a Bayesian formalism, the properties of hidden nodes can be specified subjectively, then calibrated as observed events occur. Bayesian networks are already widely used in artificial intelligence, and it was from expert systems researchers at GEC that Martin first learned the formalism.
As Martin and his team demonstrate in their June paper, and its July follow-up, ‘How dependent are defaults?’, a hidden variable need only take a few discrete values to capture the important properties of correlated defaults, while being amenable to the analytics of the saddle point method. The payout becomes apparent in the group’s third and fourth Risk papers, ‘VAR: Who contributes, and how much?’ and ‘Crossing the Frontier’. Here, Martin derives an analytic approximation for the sensitivity of portfolio value-at-risk to individual assets – which works for non-normally distributed, correlated portfolios. In his group’s final paper, he shows how portfolio optimisation can be achieved using the saddle point methodology.
For Martin’s superiors at BNP Paribas, the benefits are apparent. Although a trading book is not at first sight a loan portfolio, the counterparty credit risk associated with the firm’s derivatives positions can be viewed as a loan portfolio with stochastically varying assets (due to market risk). Xavier Pujos, chief operating officer for the firm’s fixed-income division, cites the contribution of Martin and his team: “They help us price transactions linking market and counterparty risk, and in that sense they are involved with our daily business.” The analytic techniques developed by Martin also play a strategic role, says Pujos: “It’s important to analyse our sensitivity to various events – ratings downgrades, defaults, changes in correlations, etc – so that we can manage our portfolio risks and, eventually, hedge those risks effectively and efficiently, in terms of P&L. The ultimate goal is to optimise our return on [economic] capital under the constraints we have, such as allocated capital. That’s why Richard Martin is there.” Martin praises the other members of his team, particularly Thompson, whom he says plays an important role in clarifying their ideas.
Meanwhile, Martin is commended by fellow quants. According to Mark Nyfeler, who works with the loan portfolio group for UBS in Zurich, Martin’s insights have been directly incorporated into UBS loan portfolio risk management, with outstanding results.
At CSFB, Tom Wilde – highly respected as the architect of CreditRisk+ – commends Martin for his “complex and deep work” and his “fluency in deriving formulas”. He adds: “Martin is part of a general trend in credit risk modelling, stepping back from Monte Carlo simulation and trying to better understand the risks in a portfolio. His methods are very practical, and can be readily implemented in software.”
In his current research, Martin is pursuing several avenues. He would like to see a wider discussion of the difference between subjective probability (such as systematic risk factors that cannot be hedged against) and objective probability (as implied by market credit spreads that can be used for hedging) in the portfolio risk context. He is also interested in quantifying the effect of securitisation in Basel II, and is collaborating on this with Wilde. The results are bound to be interesting. According to Wilde: “In credit risk modelling, he’s the most switched on person I know.”