Some financial optimization models: I Risk management

Abstract

Introduction Since the early seventies the domain of financial operations witnessed a significant transformation. The breakdown of the Bretton Woods Agreement, coupled with a liberalization of the financial markets and the inflation and oil crisis of the same time, led to increased volatility of interest rates. The environment of fixed-income securities, where private and corporate investors, insurance, and pension fund managers would turn for secure investments, became more volatile than the stock market. The fluctuation of bonds increased sharply after October 1979 when the Federal Reserve Bank adopted a policy allowing wider moves in short-term interest rates. According to the volatility indexes, compiled by Shearson Lehman Economics, bonds were more volatile than stocks by a factor of seven in the early eighties. Uncertainty breeds creativity, but so does a dynamic market where intelligent answers to complex problems are rewarded immediately. As a result we have seen an increased use of advanced analytic techniques in the form of optimization models for many diverse aspects of financial operations. Several theoretical developments provided the building blocks on which an analyst could base a comprehensive planning model. Models for the estimation of the term structure of interest rates, the celebrated Black—Scholes formula for valuating options, and other complex instruments, were added to the long list of contributions since Markowitz's seminal work on mean-variance analysis for stock returns in 1952.

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