Proving manipulation in the derivatives markets is tough. Regulators must provide evidence that a trader intended to manipulate markets, meaning that a case without explicit email or telephone communications to prove the motive is likely to fail.

But derivates-market overseers could take a more quantitative approach akin to that of antitrust regulators, argues Chicago Booth’s Anthony Lee Zhang. Rather than look for monopolies run by people with a stated intent to manipulate consumer prices, antitrust regulators analyze companies according to the Herfindahl-Hirschman Index, which measures market-share concentration within industries. When a company’s dominance over a sector triggers the index, regulators investigate and intervene.

There is money to be made in manipulating derivatives markets, which dwarf equity markets and the global economy. The global derivatives market represents more than $500 trillion in face value, according to the Bank of International Settlements, compared to the world’s total GDP of $88 trillion.

Investors and speculators who hold cash-settled derivatives contracts, such as futures on the S&P 500, hold positions that can generate enormous payoffs depending on the performance of the underlying index or asset. If you hold a contract that pays if the S&P 500 tanks, you might be rooting for such an outcome. You might even, if you had the means, force such an outcome by trading S&P stocks to drive the index lower. (The S&P 500 isn’t actually a likely target because it’s large, liquid, and hard to manipulate. But fraud can flourish in more obscure, less liquid indexes.)

Index values are determined by the values of the constituents in each index, and there’s no limit to the total number of derivatives contracts that can be written against any index or individual security. Regulators impose position limits, to cap how many contracts any individual trader can hold in a market, but these limits are imperfect, says Zhang. Regulators have to balance the risk of manipulation against the risk of obstructing legitimate trading, and “they don’t know how large a trader’s contract positions can be before the trader’s manipulation incentives become too large,” he says.

An investor with a big derivatives position written on a thinly traded index has a large financial incentive to manipulate the value of that index so that the contract pays off. To calculate this risk more precisely, Zhang developed a method for looking at specific derivatives contract markets to determine, like an antitrust regulator, whether a market is vulnerable to manipulation. To quantify the risk, he turned to a game-theory model that has been used to study high-frequency trading and dark pools but hasn’t before been applied to derivatives-market regulation.

Zhang also proposes a relatively simple manipulation index, which can be calculated by using the volume of derivatives contracts, the volume of the underlying market, and the largest agent’s capacity share (a technical term that can be, in some cases, tied to the size of the derivative position of the largest trader). “I propose a simple rule-of-thumb for detecting manipulable contract markets: if the manipulation index for a given market is higher than 0.7, the market is potentially vulnerable to manipulation,” he writes.

When Zhang applied this index to large and liquid markets such as the London Bullion Market Association, CME Cattle Futures, or the ICE Brent Crude Index, he found little cause to worry that contract holders are rigging markets. But the more obscure ICE HSC Basis Futures Index, which measures the difference in price between two other natural-gas-futures contracts, set off alarms.

The manipulation index could perhaps form the basis for a structural regulatory solution where regulators concentrate their attention on those markets most vulnerable to economically motivated bad actors.

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