Probability and Statistics Applied to the Practice of Financial Risk Management

This work describes applications of probability and statistics in RiskMetrics TM , J P Morgan's methodology for quantifying market risk. The methodology implements an analytical approach to nancial risk in trading, arbitrage, and investment based on the statistics of market moves in equities, bonds, currencies and commodities. The public unveiling of RiskMetrics TM in October of 1994 attracted widespread interest among regulators, competing nancial institutions, investment managers, and corporate treasurers, while the available technical documentation oers us a unique opportunity for informed statistical research on the theory and practice of nancial risk management. For the purpose of identifying problems for further research, this discussion focuses on ve applications of statistics in RiskMetrics TM , which range from data analysis of daily returns and locally Gaussian processes to stochastic volatility models and It^ o processes for the term structure of interest rates. The latter problems re BLOCKINect the author's particular interest in stochastic inference for Markov processes and multivariate dependencies. Another important theme of this discussion, however, is devoted to attracting statisticians to the study of nancial risk management and developing the foundations for collaborative w ork with nancial economists and practicing risk managers. For this reason, this is also an expository document that touches several areas of active statistical research with applications to problems of risk management.