My research spans mathematical, quantitative and statistical finance and financial econometrics. I like to work with junior colleagues, often PhD students, in a research leader role. I have worked on statistical and implied volatility models for many years, with financial applications to risk management, hedging options or hedging with futures and distribution forecasting. More recently I’ve been working on higher moments, in GARCH models, new statistical distributions, and inferring long-term realised skewness and kurtosis from daily data.
Another on-going theme of my research is to exchange-traded products with derivative-type characteristics. I have developed high-frequency pricing and hedging models that are patented and now used by market makers on the New York Stock Exchange. I am concerned by the volume now being traded on VXX — and especially on leveraged volatility exchange-traded products — because the banks that have issued them are set to make huge losses from early redemptions, when the S&P 500 eventually reverts to the level that it should be, in the absence of all the quantitative easing since the banking crisis.
Trading strategies for hedge funds has been another long-standing interest. I consult quite often in this area and some of the models that I have designed have formed the basis of popular strategies in the long-short equity category, for instance:
Alexander, Carol (1999) Optimal hedging using co-integration. Philosophical Transactions of the Royal Society A, 357 (1758). pp. 2039-2058.
Recently I have been working on developing new simulation models: Random Orthogonal Matrix (ROM) simulation and Factor Model Quantile Simulation (FMQS). The first of these papers is co-authored with my PhD supervisor Walter Ledermann and his grandson Daniel, who was my PhD student at the time. It was published on the centenary of Walter’s birth:
Ledermann, W., Alexander, C. and D. Ledermann (2011) ‘Random orthogonal matrix simulation’ Linear Algebra and its Applications 434, 1444-1467
More recent research interests are real options, network theory, cryptocurrencies and financial market manipulation and fraud. I’m currently editing (with Douglas Cumming) The Handbook of Financial Market Manipulation and Fraud, to be published by Wiley next year.