blah. First, Panos, your results would suggest that the volatility on Super Tuesday would be lower than on a random Tuesday in July when there is zero news flow.
Second, there is no reason to expect short term price movements far from expiry to be normally distributed, and thus the volatility alone is not so useful in practice.
You need to re-state your assumptions rather than forgetting about them. Of course, if you assume normal price distribution, then the options don’t provide new information.
Anonymous: The example with Super Tuesday is accurate, but represents a single prediction market. On average the markets *do* behave like the model predicts.
Perhaps you may want to read the EC’09 paper and take a look at the experimental section. You will see that reality matches our model. Additionally, is a PNAS paper named “Price Dynamics in Political Prediction Markets” published a few months back that also demonstrates similar results, also tested on real prediction markets.
You can challenge the assumptions but not reality.
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Previously: Prediction markets VERSUS Prediction markets on prediction markets VERSUS Conditional prediction markets
Why is the esteemed Stern professor spending his time and grant money studying prediction markets with ZERO VOLUME and drawing far-reaching conclusions from the results:
From the EC09 paper:
“…288,119 of 338,563 observations that we
have (i.e., > 85% of the whole dataset) had zero price change
since the previous day. Moreover, 287,430 of these observa-
tions had zero daily trading volume, what means that most
of the time price did not change because of the absence of
any trading activity.”
Of course, if you heavily bias your data set towards contracts with ZERO daily volume, then volatility will tend to be determined largely by the time to expiry: people only start trading them when they are about to expire.
Perhaps the model is valid, I don’t know, but this is a low-quality paper, and to make such sweeping conclusions based upon it is dangerous.
What is more dangerous is that this field, for all its promise, lacks critical mass of very bright people in its practice and study, making papers such as this more likely to be taken seriously by the good-willed amateurs, media and other interested parties who lack critical reading skills.
Last, Panos has reiterated the over-reaching conclusions on his personal blog as if they are accepted and established, without any mention of the problems with the data set, the inherent assumptions, or the resulting limits to the model’s applicability.
e.g.: “Our work shows what the exact form of future price distributions, without the need to provide any volatility estimates.”
No. What the esteemed professor has done is provide a Brownian model that allows one to replace the measured historic volatility with a volatility that is derived solely from price and time to expiry. Neither of these methods are very good, as they are both rife with simplifications that make the problem tractable in the first place. And, critically, whether or not Panos’ model is the better or worse of the two is an open question.
Everything interesting happens in the tail. You can’t assume the tail doesn’t exist, solve the problem, compare your model with shoddy data, then tell the world you have cracked the nut.
I’m glad this blog is here to help shed light on the dirt under the table.
I am a co-author of the paper. Just want to make few comments to resolve possible misunderstandings:
1. We did not bias the dataset towards days with zero trading volume, in fact, we exclude such days from the estimation equation. Unfortunately, due to space limitations, this information was dropped from the EC’09 paper, however it is still in the working version of the paper on SSRN:
“Results of this regression are given in the Table 2, standard errors are corrected for heteroscedasticity. Note that we included zero deviations (but not zero volume trading days), but to avoid taking logs of zero we added a small smoothing factor (10^{-4}) under the log(|a_t|).”
Moreover, we have performed a number of robustness checks, in particular, we tested the model only on a set of 51 presidential election contracts; most contracts in the set were much more liquid than an average InTrade prediction market.
2. There is indeed a lack of high quality statistical research on prediction markets. I have seen published papers doing terrible things like regressing prices from one prediction market on prices in a different prediction market and constructing standard errors for such regression as if prices represent i.i.d. sequences. Our paper was in fact an attempt to show that neither prices nor returns in a prediction market can be treated as i.i.d. sequences.
3. The goal was to come up with a simple but useful model of volatility. The fact that we have a closed form non-parametric expression for volatility definitely comes at a price of making some unrealistic assumptions. We could have done something way more advanced like stochastic volatility model or a more generic Levy process with jumps to model the market evolution: we would not have gained better understanding of how market volatility evolves but only lost beauty of the final result. Simplicity is still an important determinant of the success of financial models. You’re welcome to try and extend (or even completely replace), what we’ve done. We will be happy to provide the full dataset that we have, just mail me or Panos and we can send you the Excel files with data.
4. The main problem with modeling return properties in a prediction market is that a lot of prediction markets are very short and lack enough historical data. That harms performance of even simplest volatility models like GARCH and that’s why our “dumb” model actually outperforms GARCH on most of the contracts, even liquid ones.
Dear anonymous:
Please be eponymous and read the paper carefully. I have no problem with criticism. I blogged about the paper before it was published. Jason Ruspini and David Pennock jumped in and pointed to problems. We incorporated their suggestions and the paper ended up being better at the end. I knew their background and I trusted their suggestions.
Jason Ruspini gave comments on historic volatility vs analytic form. Good point, and we added that in the paper. We compared our model with GARCH (historic volatility), and we presented a hybrid that works better than both of them. So, I have the answer to “whether or not Panos’ model is the better or worse of the two is an open question.” It is a closed question. It is worse.
Regarding the validity of the model: Do not trust a single paper? Good. I would not trust a single paper either. But please read the PNAS paper as well. You will see that they have a very different model in their approach. Well, surprise: their final equation is strikingly similar to ours. They even used completely different markets. I was very happy to see such independent reproducibility. What else do you need to see to be convinced that the model works?
Limitations? Discussed in the paper, Section 5. As you already mentioned, the returns do not follow a Gaussian. I agree. Incorporating a log-normal distribtuin is directly possible. See Section 3.3. You want power-law distribution of returns? Combine the Gaussian with a Poisson jump model. (See Section 5).
If you know prediction markets with significantly higher liquidity than Intrade, please let us know. We would love to work with such contracts.
Regarding the low volume, I would actually turn that around: There is no significant flow of information early on (what can you tell about the 2016 presidential election now?), and hence the probabilities do not change, and therefore there is no trading.
And to restate my conclusion: Having options on stocks is more useful than having options on prediction market contracts. Trading options on stocks generates estimates of the implied volatility of the share price. Trading options on prediction markets does not give the same amount of information.
Finally: “Panos has reiterated the over-reaching conclusions on his personal blog as if they are accepted and established, without any mention of the problems with the data set, the inherent assumptions, or the resulting limits to the model’s applicability.” Guilty as charged. But I assume that people will actually read the paper, if they find the blog post interesting. Assumptions and limitations are discussed there. Just discussing the limitations of the approach would be as length as the whole post. It is not that we are hiding the limitations or “hiding the dirt under the table”. There is a freaking section in the paper, titled “Limitations”.