Mathematics Achieves Command of Financial Risks

Financial Mathematics


Dr. Peter Cotton

Peter's interest in applied probability may stem from an early fascination with games of chance and beating the odds. He wrote optimal bet allocation programs for a professional handicapper in Sydney and maintains an interest in the mathematics of sports. His undergraduate training was in physics and mathematics at the University of New South Wales (conveniently located opposite the main venue for horseracing in Sydney).

Peter first became interested in financial mathematics while completing a Ph.D. in the Mathematics Department at Stanford University, supervised by Professor George Papanicolaou. His first theoretical introduction came from Stanford Business School Professor Darrell Duffie's dynamic asset pricing lectures ,and his first practical taste of real world risk management came shortly thereafter working at Morgan Stanley in the summer of 1998. Banks were scrambling to assess their exposure at this time, a sharp fall in oil prices having led to collapse of the Russian bond, stock and currency markets.

Peter's interests include the mathematical modeling of over the counter financial securities. Deals made between banks and clients can be arbitrarily complex, and collectively form a largely opaque world of similar but non-identical securities. Financial models effect a glorified interpolation of the relative prices of these bets and their relationship to more frequently traded standardized securities. In principle, financial models also provide an early warning radar system alerting managers to possible disaster but unfortunately, advances in financial mathematics have not kept pace with financial innovation. Many have suggested that this failure contributed in no small way to an apparent securitization bubble whose collapse threatens the economy at large.

Julius Finance brings a new slant to financial risk management which acknowledges the fundamental limitations of humans and their "hand made" financial models. Classic financial mathematics techniques (parametric models, PDE methods) have proven tremendously useful when applied to low dimensional problems, but their obvious extensions to complex high dimensional financial markets are difficult to get right (too often the models fail to calibrate or reflect market realities). Elaborate constructions and great inventiveness would be required to simultaneously model thousands of financial securities and this probably exceeds reasonable human abilities.

In response, Peter's research has focused semi-automated financial model construction - a combination of man and machine. The company pioneers model fusion technology, a collection of techniques for non-trivial combination of financial models with overlapping domains. With fortuitous timing, the company is commercializing a unified credit model at the height of the credit crisis.

Previously, Peter was a Vice President at Morgan Stanley where he built correlation trading tools and managed a dedicated research effort into mathematical models for credit markets. Numerous leading academics contributed insights into a central problem of credit risk management, namely the construction of plausible dynamics models for the evolution of credit market prices.