Simone Calogero: “A First Course in Option Pricing Theory”

In the context of science and technology we are used to employing sophisticated mathematical methods.Even more so, many concepts owe their very existence to applications in these areas.And thankfully, this has the effect that the graduates of what is perhaps the most abstract of all sciences find enough employers who are willing to afford them a decent living in the real world.Many business administration students are painfully aware of the fact that you should also have a certain affinity for numbers in the realm of finance and business.However, we are not usually talking of difficult maths here.This fact perhaps explains the hype surrounding the much more demanding area of modern mathematical finance, whose triumphal march began in the early 1970s, together with the establishment of derivatives exchanges.And even though a certain degree of disillusion has taken hold in the wake of various financial crises, sums that exceed Germany's annual gross domestic product are still being turned over every day on the basis of complex mathematical models.Louis Bachelier's doctoral thesis from 1900 can rightly be viewed as the birth of both mathematical finance and Brownian motion.But it initially received little attention.Itō's work, on the other hand, played a greater role in the further development.Although he regarded himself as a pure mathematician, his stochastic integral, conceived in seclusion in Japan, became indispensable for modern financial mathematics.It still amazes me how well prepared the thriving theory of stochastic processes proved to be for the upcoming requirements of financial market modelling.The reverse development, i.e. the stimulation of stochastic analysis by financial applications, only set in quite late.Ironically, it was largely driven by Soviet-socialised Eastern European mathematicians and their partly leftist Western peers who were rather