The meaning of implied volatility in pricing stock options traded in options markets

Ph.D. in the Faculty of Business Administration

Tribes under threat : the collective behavior of firms during the stock market crisis

Due to their unpredictable behavior, stock markets are examples of complex systems. Yet, the dominant analysis of these markets as- sumes simple stochastic variations, eventually tainted by short-lived memory. This paper proposes an alternative strategy, based on a stochastic geometry defining a robust index of the structural dynamics of the markets and based on notions of topology defining a new coef- ficient that identifies the structural changes occurring on the S&P500 set of stocks. The results demonstrate the consistency of the random hypothesis as applied to normal periods but they also show its in- adequacy as to the analysis of periods of turbulence, for which the emergence of collective behavior of sectoral clusters of firms is mea- sured. This behavior is identified as a meta-routine.