Prof. Jayanth R. Varma’s Financial Markets Blog

A blog on financial markets and their regulation

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.

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