Sunday, July 13, 2008

Options Markets for Prediction Markets?

Over the last few months, together with George Tziralis, we have been doing research on the efficiency of the prediction markets.

At the very basic level, we want to examine how fast the market can incorporate into the price of a contract all the available information. Our experiments, so far, on InTrade show that the price of a contact tends to be "unpredictable" when using purely historic price data. In other words, the markets on InTrade tend to be "weakly efficient".

In fact, some pretty extensive time-series tests showed that the price movements are almost a random walk. Furthermore the spectrum of the random walk movements (after doing a Fourier transform) tends to be something close to 1/f noise (or pink noise). Assuming that each price change indeed captures the effect of a real-time event (this is a big assumption), then we can conclude that the importance of the events that happen tends to follow a "power-law": there is the "big" events that move the market significantly, but there is also a large number of minor events that cummulatively can move the market significantly, even though none of them is of any particular importance.

The next question that we wanted to examine, was whether the price changes have the same importance in different times. By analyzing the markets we observed that the prediction markets, just like the financial markets, exhibit the phenomenon of volatility clustering. In other words, there are periods in which the market tends to move up and down a lot, and periods in which the prices are relatively stable.

What are the implications of this findings? If we want to assign an importance value in a price change, we have to take into consideration the (past and future) volatility of the prices. Going from 60 to 80 in a period of low volatility signals a much more important event compared to the case of going from 60 to 80 in a period of high volatility.

With George, using the general family of the ARCH models we showed that we can model and predict nicely the volatility of the markets, and we can then estimate properly the importance of the events that correspond to these price changes.

Even though such models are good, there are limits on their predictive power.

A much better approach for estimating the future volatility of a market is to allow people to directly trade volatility. In financial markets, this happens by allowing people to buy options for a given stock. The values of the options give a good idea on what is the expected, future volatility of a stock (and its expected upward or downward movement). Therefore, having options allow us to estimate how robust and stable a particulat contract will be in the future.

In principle there is nothing that prevents us from having such derivative markets on top of the existing prediction markets. For example, we could have contacts such as "Obama@0.80/01Sep2008", which would allow people to buy for 0.80 cents, on September 1st 2008, a contract for Obama winning the presidency. If the actual contract is trading above 80%, the contract will turn a profit. (This is exactly equivalent to the existing options for stocks.)

The prices of such options give a good estimation of how volatile the contract is going to be in the future. For example, if Obama is trading today at 0.65 and noone is willing to buy the 0.80 contract for September, then traders do not believe that Obama will reach that level by September. On the other hand, if the price of the "Obama@0.80/01Sep2008" call option trades at 0.05, then people believe that the contract has good chances of being above 0.05 by September.

Using such values we can estimate the "upside volatility" of the contract. (The corresponding "put" contracts will show what is the estimated volatility on the downside.)

Of course, while such ideas are nice, we should not forget that markets work only when there is liquidity. And given the relatively low liquidity for the existing, primary prediction markets, there is little hope that such derivative markets for "options on prediction markets" will have even close to the necessary liquidity.