the black swan the impact of the highly improbable

The first reason is an increased frequency and intensity of the occurrence of extreme events. There has been an on-going interest in extreme events throughout the centuries for various reasons. On the other hand, extremely high water levels could also lead to disaster by flooding both the harvest fields and the places of the population. Therefore, extremely low water levels could directly cause bad harvests, which could consequently lead to famine. Agriculture in the region of the Nile delta was dependent on fertilizers and water from the Nile mud. The water levels were precisely recorded and due to their importance to the Egyptians, whose economy and welfare in the environments surrounding the Nile were dependent on its water level.

The first known and documented research that dealt with extreme events and their causes focused on water levels of the Nile 5000 years ago in Egypt.

Their distinction is due not to the scale of disaster and destruction, but rather to the extreme low probability, unpredictability, infrequency and massive impact of the events. The Vulcan eruption of Pompeii, the Arab Spring, the stock market crash of 2007-2008, and the Fukushima Daiichi nuclear disaster are all distinctive events. Key Words: Option pricing formula, systemic risk, financial crisis, and derivative securities This paper examines the questions and criticisms raised by a significant number of financial economists about the weaknesses or the flaws in the Black-Scholes-Merton option-pricing-formula and related mathematical models. The increased complexity of these securities coupled with trillions worth of high-leverage transactions, instead of reducing the risk as surmised in the theories, amplified the risk in the markets that eventually led not only to the global financial crisis of 2008 but also to the ongoing worldwide systemic risk. According to several financial economists, the origins of this menagerie of derivative securities, can be traced to the Black- Scholes-Merton option-pricing-formula and a host of other related mathematical models. In recent years, large financial institutions attempted to outwit the markets and eliminate risk by creating and trading enormous volumes of a variety of derivative securities such as Mortgage-Backed Securities (MBS), Collateralized Debt Obligations (CDO), and Credit Default Swaps (CDS),etc.

The black swan the impact of the highly improbable