The Mathematics of Financial Models: Solving Real-World Problems with Quantitative Methods

CHAPTER 1 Setting the Stage

 

Since the seminal Black-Scholes and Merton papers in 1973, the derivatives market has exploded by leaps and bounds. Derivatives are now being traded in esoteric asset classes like weather, mortality, credit, and real estate—just to name a few. While reasons for this development can be attributed to a myriad of factors, including taxes, market inefficiencies, creativity in product development, advances in financial modeling, investor sophistication, and so on, it is undeniable that the single biggest motivation for the existence of the current state of affairs in the derivatives market is the existence of sophisticated market participants. This, fueled by a flurry of publications on risk-quantification techniques, led investment banks in the late 1970s and early 1980s to employ mathematicians, physicists, and engineers with PhDs as their in-house rocket scientists or quants or eggheads. Thus began the migration of academics to the lucrative world of finance (who, at that time, were struggling to find decent university positions in their respective fields of mathematics, physics, and engineering). As a consequence, the field of financial economics grew exponentially in mathematical complexity, with practitioners beginning to question the assumptions underlying the Black-Scholes model in the hope of building a more realistic model that would give them a better competitive advantage.

After the 1987 stock market crash and a series of highly publicized ...