"partial differential equations have become the core tools in a discipline that previously relied on a collection of anecdotes, rules of thumb, and shuffling of accounting data."
The role of mathematics in generating wealth
Derivatives market: the rise of the derivatives
market is one of the most important financial phenomena in the recent
history of the financial markets. Its expansion has been spectacularly
rapid and large [see chart, note it only traces the growth of one class
According to Allbusiness.com, The evolution of financial derivatives during the past two decades ‘is related to the fundamental changes that have occurred in the financial markets. Innovations in financial theory and increased computerization, along with changes in the foreign exchange markets, the credit markets and the capital markets over this period, have contributed to the growth of financial derivatives’2. Since financial theory is essentially mathematical, an enormous wealth has been generated thanks to the application and understanding of the mathematics behind futures and options pricing. Even more interestingly, Robert Merton, the co-author of the famous Black-Scholes equation, admits that the equation was developed with “essentially no reference to empirical option pricing data as motivation for its formulation”3 , it was a pure mathematical derivation based on past work by Louis Bachelier, Kiyoshi Ito and others. Despite of its theoretical character, his research determined future practices in the financial world. As Merton puts it “stochastic differential and integral equations, stochastic dynamic programming, and partial differential equations have become the core tools in a discipline that previously relied on a collection of anecdotes, rules of thumb, and shuffling of accounting data”4. The success of the Black-Stokes model was so great that Texas Instruments was selling calculators with the model pre-programmed only two years after its publication. Eventually, further research in pricing models increased the efficiency and the scope of the algorithms used and generated an almost unlimited range of innovative derivative products that are constantly launched on the financial markets.
SERAFIM Ltd and Mathematics
Our white papers (accessible from the menu on the left) demonstrate our achievements in the use of mathematics in the fields of our interest. Moreover, Serafim FUTURE, our Integrated Asset Model for Reservoir Engineers, offers a number of innovative algorithms that help numerous Reservoir Engineers around the glob with their day-to-day work.