16 CHAPTER 1. BACKGROUND IDEAS
year.
Financial events since late 2008 show that many of the concerns of the
previous paragraphs have occurred. In 2009, Congress and the Treasury
Department considered new regulations on derivatives markets. Complex
derivatives called credit default swaps appear to have been based on faulty
assumptions that did not account for irrational and unprecedented events, as
well as social and cultural variables that encouraged unsustainable borrowing
and debt. Extremely large positions in derivatives which failed to account
for unlikely events caused bankruptcy for financial firms such as Lehman
Brothers and the collapse of insurance giants like AIG. The causes are com-
plex, but some of the blame has been fixed on the complex mathematical
models and the people who created them. This blame results from distrust
of that which is not understood. Understanding the models is a prerequisite
for correcting the problems and creating a future which allows proper risk
management.
Sources
This section is adapted from the articles “Influence of mathematical mod-
els in finance on practice: past, present and future” by Robert C. Merton
inMathematical Models in Financeedited by S. D. Howison, F. P. Kelly,
and P. Wilmott, Chapman and Hall, 1995, (HF 332, M384 1995); “In Honor
of the Nobel Laureates Robert C. Merton and Myron S. Scholes: A Par-
tial Differential Equation that Changed the World” by Robert Jarrow in the
Journal of Economic Perspectives, Volume 13, Number 4, Fall 1999, pages
229-248; and R. Jarrow and P. Protter, “A short history of stochastic inte-
gration and mathematical finance the early years, 1880-1970”, IMS Lecture
Notes, Volume 45, 2004, pages 75-91. Some additional ideas are drawn from
the article “Can Numbers Ensure Honesty? Unrealistic Expectations and the
U.S. Accounting Scandal”, by Mary Poovey, in theNotice of the American
Mathematical Society, January 2003, pages 27-35.
Problems to Work for Understanding
Outside Readings and Links:
- History of the Black Scholes Equation Accessed Thu Jul 23, 2009 6:
AM