Oxford: Princeton University Press. March 29, , is considered by many to be the day mathematical finance was born. On that day a French doctoral student, Louis Bachelier, successfully defended his thesis Theorie de la Speculation at the Sorbonne. The jury, while noting that the topic was far away from those usually considered by Bookseller: Ria Christie Collections , Greater London, United Kingdom Seller rating:.
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Carl Friedrich Gauss Mathematician. Ethics in quantitative finance. Sign in. In fact, Bachelier did have the right approach, although not the complete answer, to the option pricing problem—and at least as good an answer as anyone for fifty years afterwards—and his service to posterity was to point Samuelson and others in the right direction at a time when the mathematical tools needed for a complete solution were lying there waiting to be used. Didn't find what you're looking for? Hermann Weyl Mathematician. Remember me on this computer.
An intensive period of development in financial economics followed, first at MIT and soon afterwards in many other places as well, leading to the Nobel Prize-winning solution of the option pricing problem by Fischer Black, Myron Scholes and Robert Merton in Within a decade, option trading had mushroomed into a multibillion dollar industry. Expansion, both in the volume and the range of contracts traded, has continued, and trading of option contracts is firmly established as an essential component of the global financial system. In this book we want to give the reader the opportunity to trace the developments in, and interrelations between, mathematics and economics that lay behind the results and the markets we see today.
It is indeed a curious story.
On the mathematical side, things were very different: Bachelier was not at all lost sight of. He defined Brownian motion and the Markov property, derived the Chapman—Kolmogorov equation and established the connection between Brownian motion and the heat equation. Much of the agenda for probability theory in the succeeding sixty years was concerned precisely with putting all these ideas on a rigorous footing. Did Samuelson and his colleagues really need Bachelier?
Yes and no. The parts of the subject that really did turn out to be germane to the financial economists—the theory of martingales and stochastic integrals—were in any case later developments. Yet when the connection was made in the s between financial economics and the stochastic analysis of the day, it was found that the latter was so perfectly tuned to the needs of the former that no goal-oriented research programme could possibly have done better.
Bachelier had attacked the option pricing problem—and come up with a formula extremely close to the Black—Scholes formula of seventy years later—using the methods of what was later called stochastic analysis.
He represented prices as stochastic processes and computed the quantities of interest by exploiting the connection between these processes and partial differential equations. He based his argument on a martingale assumption, which he justified on economic grounds. Samuelson immediately recognized that this was the way to go. And the tools were in much better shape than those available to Bachelier. From an early twenty-first century perspective it is perhaps hard to appreciate that an approach based on stochastic methods was a revolutionary step.
It goes back to the question of what financial economists consider to be their business. In the past this was exclusively the study of financial markets as part of an economic system: how they arise, what their role in the system is and, crucially, what determines the formation of prices. The classic example is the isolated island economy where grain-growing farmers on different parts of the island experience different weather conditions. Everybody can be better off if some medium of exchange is set up whereby grain can be transferred from north to south when there is drought in the south, in exchange for a claim by northerners on southern grain which can be exercised when weather conditions in the south improve.
In a market of this sort, prices will ultimately be determined by the preferences of the farmers how much value they put on additional consumption and by the weather.
To take a purely econometric approach, i. Understandably, any such idea was anathema to right-thinking economists. When considering option pricing problems, however, the situation is fundamentally different. The option pricing problem is not to explain why the price ST is what it is, but simply to explain what is the relationship between the price of an asset and the price of a derivative security written on that asset. It is not bundled up with any explanation as to why the underlying asset process takes the form it does.