Manipulating Closing Prices: The randomization antidote

Manipulation of closing pricing appears to be happening in some of the most liquid markets in the world, and randomization might be the most effective antidote to the problem. I blogged about Amaranth’s manipulation of Nymex natural gas closing prices last week. Dealbook talks about an episode in Blackstone’ shares:

Units of Blackstone ... nosedived for much of the day, dipping as low as $23.27, down 8.8 percent from Wednesday’s close of $25.51, by mid-afternoon. But a mysterious frenzy of trades just before the market’s close helped erase the entire day’s losses and push the stock up to $25.70.

Starting in the last 10 minutes, a series of rapid-fire buy orders helped push up the stock’s price. Among them was a block trade of 114,000 units, which was one of the biggest trade of the day. The time? It was executed at 3:59:55 p.m.

Averaging the last few minutes of trading helps but not completely because the manipulator knows the averaging algorithm used by the exchange. The key insight in my view is to think of this as a game between the exchange and the manipulator in which the exchange moves first and the manipulator can decide his response accordingly.

Game theory would suggest that the exchange use a mixed strategy involving randomization of the time slots over which averaging is done. This neutralizes the advantage that the manipulator has in the current system of moving second. The random time slots could be chosen by sampling from say a beta distribution with shape parameters alpha>1 and beta=1 that produces an increasing probability density function. This would ensure that most time slots would be from the final minutes of trading, but occasionally, there would be a time slot from earlier in the day.

Using public key encryption technology, it is possible for the exchange to announce the actual time slots resulting from the random sampling in advance in a manner which is verifiable ex post but not readable ex ante. This ensures that the exchange cannot manipulate the sample either.

Posted at 2:24 pm IST on Tue, 31 Jul 2007         permanent link

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