Over the past 50 years or so, financial economists have developed a set of increasingly complex and sophisticated mathematical models for the behavior of financial markets and for the value of the financial instruments (stocks, bonds, currencies, and more exotic “derivatives” thereof) traded in financial markets. Over perhaps the past 35 years, with exponential growth in computing power, there has been an explosion in the application of these theories to practical management of investments and of the financial underpinnings of many businesses. New financial instruments created by using the theories have come to rival (some would say overwhelm) traditional financial markets in some sectors.

Perhaps surprisingly, behind the enormous complexities of these theories and of their applications, there often stands an extremely simple, even simple-minded, set of little assumptions about how markets ought to work, and how people ought to value financial instruments. The talk will try to uncover the simple-minded core assumptions behind two of the theories in constant use: the Capital Asset Pricing Model for the risk/reward equilibrium values of financial instruments in the market and the Risk-Neutral Pricing Model for a “derivative” financial instrument (one whose value “derives” in some way from the value of another financial instrument). Little more than some calculus, vector-space geometry, and probability theory will be used