The development of modern financial markets can be traced back to two events in the USA in 1973, both of which revolutionised market practice, for very different reasons. One of these revolutions was essentially institutional: the opening of the world's first options exchange in Chicago allowed options to be exchanged in much the same way as stocks (that is, through a regulated exchange) rather than having to be traded ‘over the counter’ as separate contracts between buyer and seller. The second upheaval was purely theoretical: the publication in the Journal of Political Economy of the now famous paper by Fischer Black and Myron Scholes (extended by Robert Merton in the same year), which developed arbitrage techniques for pricing and hedging options, and presented the now ubiquitous Black-Scholes formula for the rational pricing of European call options.

By the late 1970s the basis of their arguments, and the link with martingale theory in particular, had become well enough understood to allow the rapid development of this theoretical breakthrough, which has, since the 1980s, pre-occupied a host of financial economists and mathematicians (principally probabilists) and has given rise to the new profession of quantitative analyst (or ‘quant’), which has attracted into the finance sector a large section of the best graduates with mathematics, physics, statistics or computer science degrees. This, in turn, has spawned a host of postgraduate courses emphasising market practice and taught in business schools, but increasingly also courses attached to mathematical sciences departments, focusing on the underlying mathematics, much of which is of comparatively recent origin.