Research & Innovation

Black Swans vs. Financial Engineering

As a boy growing up in Damascus, Syria, Khaldoun Khashanah found mathematics compelling. “What I liked best were the abstract patterns, and math’s ability to reveal the interrelations between the real and the abstract in unique ways. Math lets us look through that window,” Khashanah explained.

Maybe that is why Khashanah, the director of Stevens Institute of Technology’s Financial Engineering program, has a problem with Black Swans.

Black Swans are those seemingly impossible, game-changing events popularized by Nassim Nicholas Taleb in his 2007 book, The Black Swan. Taleb picked the name because Europeans thought all swans must be white, until they discovered black swans in Australia during the Eighteenth Century.

According to Taleb, a Black Swan has three characteristics: First, it is so rare, “nothing in the past can point convincingly to its possibility.” Second, it has very high impact. Third, people “concoct explanations for its occurrence after the fact, making it explainable and predictable.”

To Khashanah, Taleb’s focus on the unpredictable nature of Black Swans seems to fly in the face of everything he knows about the ability of mathematics to find patterns in the world around him.

“Taleb does not identify the current financial meltdown as a Black Swan, even though it appears to meet his own definition of a Black Swan,” Khashanah said. Banks were shocked by how badly risk models underestimated their vulnerability. The result upended the global economy. In retrospect, everyone says we should have seen the signs.

“Still, you cannot tell me that whole financial system had no information that could have warned us about subprime mortgages and derivatives, that the crisis was just random. I don’t buy that,” said Khashanah, who is also a Distinguished Service Professor at Stevens.

“As a field, Financial Engineering is presented with two choices. We can either stop producing risk models because the phenomenon is too complex, or face up to that complexity and try to incorporate it within a new modeling paradigm. I choose the latter.”


For Khashanah, facing up to uncertainty involves financial engineering, building models that help investors minimize the risk on their investments.

Like many people drawn to the field, Khashanah’s passion for mathematics led to engineering and more mathematics. He eventually earned a Ph.D. in applied mathematics at University of Delaware. In 1994, he joined Stevens as a visiting researcher, developing formulas to help sonar tell the difference between echoes and mines in shallow water.

At the time, many physicists and mathematicians had begun to gravitate towards financial modeling. Khashanah followed. “Financial modeling poses many deep mathematical problems, and the remuneration was also very good,” he said.

At the time, financial modeling was coming into its own, especially in the field of derivatives. Derivatives are securities based on the price of an underlying asset. An example is an option, which is the right (but not the obligation) to sell a stock at a specific price, either higher or lower, at a specific time in the future. The price of the option is derived from the price of the stock, and the two rise and fall in harmony.

Wall Street frequently uses derivatives to reduce risk. Suppose a trader buys a stock because he or she expects the price to rise. The trader can offset, or hedge, the risk of the stock going down by buying an option to sell at a specific price (called the strike price).

If the stock drops below the strike price, the trader buys the now- cheap stock on the market and sells it for the higher strike price at a profit. If the stock goes up, the trader takes the profit and lets the option expire.

Because derivatives cost much less than the underlying asset, they are highly leveraged. A small move in the price of the underlying asset can yield a large profit – or loss.


Simple derivatives, like stock options and commodity futures for crops, metals, and currencies, have existed for more than 100 years. High-speed computerized modeling broadened their use.

Starting in the 1980s, traders created mathematical programs to analyzed trends and bought and sold stocks (and options) within seconds. In the 1990s, financial firms broadened their use of derivatives to cover everything from credit card debt to home mortgages.

“Starting around 2000, those derivatives began growing more complicated,” Khashanah said. On Wall Street, firms began to slice up mortgages and reassemble the pieces into tradable securities called collateralized debt obligations, or CDOs. The goal was to combine conventional, subprime and other low-risk mortgages to minimize risk.

Although it was very difficult to assess the amount of risk in those CDOs, financial firms like AIG continued to write derivatives on them. This created what Khashanah calls a “super-portfolio” of mortgage-backed securities and derivatives used to hedge them.

“The subprime mortgages were worth several hundred billion dollars, but the CDOs and derivatives were worth trillions of dollars,” he noted.

When super-portfolio bubble burst, the size of the liabilities was large enough to shake the entire financial system. The impact was certainly a Black Swan-level impact.

Where did risk models go wrong? According to Khashanah, models fail for three reasons: wrong hypotheses; poor models of the phenomenon they try to explain; and inaccurate data, which can sink even the most accurate model. While all models suffer some deficiencies in all three areas, Khashanah points to inaccurate data as a key culprit in the financial crisis.

“Data inaccuracies were due to a total lack of transparency in the derivative space over a long period of time. This misinformation was passed on as credible input to models to analyze,” Khashanah said.

“Granted, the models were simplistic when compared to the complexity of the instruments, and they barely satisfied their own hypotheses. But even if we had perfect models, misinformation results in mischaracterization.

“As a result, no one knew the actual size of these super-portfolios or the true liabilities of the big banks. They were enormous, and there was no way to pay all these liabilities when they came due. That is why the government had to bail them out,” Khashanah concluded.


In many ways, this sounds like a Black Swan. The collapse of the market was a tsunami that came out of nowhere and had devastating results. Although few saw the signals early, everyone can now look back and see why it happened.

“Yes, the models did not capture enough of the system’s complexity,” Khashanah said. “But the Black Swan goes to the other extreme. It says that since the models were wrong, you cannot believe in any models.”

“I cannot accept that,” he continued. “If you accept that only random events count, you cannot build a science. That is what we are trying to do, build a science of financial risk management.

“It’s not easy. It’s like when we test a new drug to determine if it is safe and effective. Sometimes the testing methodology fails, but no one would reject that methodology unless we had something better.”

The key, Khashanah continues, is to look at the problem as a systemic problem and then assess how models have to change to capture the right type of information.

At the system level, that starts with greater regulation and more transparency. “The systemic risk was unregulated activities coupled with lack of transparency. This made all calculations of risk misleading,” Khashanah said. “If we had data about the size of the banks’ super-portfolios, we would have understood the risk much better.”

Financial modelers also have to do a better job of identifying risks they have never encountered before. This is especially true during periods of innovation.

“Black Swans are often associated with market innovations, such as collateralized debt obligations and complicated derivatives or, to go back a little further, businesses and automated trading,” Khashanah said.

“The market packages and sells those innovations very quickly, and regulations don’t have a chance to catch up. If the regulators are only looking for problems they expect to see, they miss the issues with those innovations. They continue to accumulate within the system, and when the system bursts, those problems seem to come out of nowhere,” Khashanah explained.

Finally, modelers need to find a way to balance quantitative models with qualitative information. “Our models of the financial system are not like our models of nature. In nature, there is no escaping the laws of physics, and so our physical models are very accurate,” Khashanah explained.

“But you can’t expect people to follow your equations. People may feel optimistic, or they may react to a sudden drop in prices with panic selling. They are impacted by politics, economics, social theories, rumors, and regulations.

“The reason the derivatives bubble went on for so many years was that people thought they were managing risk. They were confident. When they discovered that they were vulnerable, they panicked and the financial system went into freefall.

“As modelers, we need to find a better way to reflect those qualitative components in our models. Instead of taking a narrow, reductionist approach, we have to consider the larger system – from innovation, regulation, and information flow to technology and new financial products – and continuously monitor systemic risk.”

Khashanah paused, then continued: “Some people think it is better to live without models than to have lousy models. They believe those rare game-changers – Black Swans – matter and discard ordinary events. To make a fortune, you should invest only after a Black Swan.

“That’s not what the financial system should do. It is about making everyday investments that give companies and the economy the liquidity they need to innovate and grow. If we want progress, that is the only way to invest. Ultimately, models can help us do that by reducing the risk of our investments.”

Alan S. Brown is a science writer and blogger who serves as associate editor of Mechanical Engineering magazine.