Thursday, October 05, 2006

Arbitrage in Prediction Markets

One of the interesting things about the IEM Congessional Control Markets is that there are lots of different ways in which to take a position on an event. So, for example, if you want to bet on the event that Democrats take control of the House, there are four ways to do it: (i) buy RH.lose06 in the House06 market, (ii) buy a fixed price bundle and then sell both RH.gain06 and RH.hold06 in the House06 market, (iii) buy both NH_RS06 and NH_NS06 in the Congress06 market, or (iv) buy a fixed price bundle and then sell both RH_RS06 and RH_NS06 in the Congress06 market. In a thick market with heavy trading and optimal behavior on the part of traders, these four different ways of entering the same position should cost the same. But these are thin markets with varying degrees of sophistication among participants, so prices across contracts and markets are sometimes not mutually consistent.

In fact, sometimes prices get so misaligned that there appears an opportunity for aribrtage: one can take a combination of positions that yields a sure profit (regardless of what happens in the election). Consider for instance the prices as of 7:30 CST this morning:
07:30:00 CST, Thursday, October 05, 2006.

Symbol Bid Ask Last
RH_RS06 0.445 0.460 0.430
RH_NS06 0.031 0.045 0.031
NH_RS06 0.300 0.315 0.320
NH_NS06 0.208 0.235 0.207

Symbol Bid Ask Last
RH.gain06 0.022 0.039 0.022
RH.hold06 0.516 0.534 0.520
RH.lose06 0.455 0.515 0.462

At these prices, a trader could bet on Republican loss of the house in the House06 market and simultaneously bet on Republicans maintaining control of the house in Congress06 for a sure profit. Selling RH.gain06 and RH.hold06 in the House06 market, and selling NH_RS06 and NH_NS06 in the Congress market has a total net cost of $0.954 per contract. Whathever happens on November 7, the positions in one market will expire at $1 while positions in the other will expire worthless. So you're buying $1 for a $0.954 on each set of contracts traded in this way.
Nobody is going to get rich looking for opportunities such as this, which is why it's so easy to find them. But this example is a nice way to see the logic underlying arbitrage based pricing relationships such as the put-call parity theorem.

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