# Penoc options trading

Robin Hanson invented a wonderful market maker well suited for use in prediction market applications with a long name: In fact, Hanson invented an entire class of market scoring rule market makersbut the logarithmic variant seems the most useful. As Chris Masse is quick to point outLMSR has achieved much more widespread use than my own competing invention, the dynamic parimutuel market makerwhich so far is being used in only one place: In this post I will try to explain how to implement LMSR in a way that I believe most people familiar with prediction markets will understand.

This interpretation of LMSR is not new: Suppose there are two outcomes that traders can buy or sell shares of bet on or against such that one and only one of the two outcomes is guaranteed to eventually occur. The market maker keeps track of how many shares have been **penoc options trading** by traders in total so far for each outcome: The market maker also maintains a cost function C q1,q2 which records how much money traders have collectively spent so far, and depends only on the number of shares outstanding, q1 penoc options trading q2.

For LMSR, the cost function is:. Traders arrive one at a time and tell the market maker how many shares they want to penoc options trading or sell of each outcome. The market maker uses the cost function to answer these questions.

If this amount is negative it means the trader receives money instead of paying money. A trader arrives who wants to buy 10 shares of outcome 1.

The trader must pay:. Now the same trader above returns to the market and wants to sell her 10 shares. The current price for outcome 1 is:. But note that the current price only applies for buying a miniscule infinitesimal, in penoc options trading number of shares. As soon as a trader starts buying, the price immediately starts going up. In order to figure out the total cost penoc options trading buying some number of shares, we should use the cost function C, not the price function.

If you remember your calculus: But if unfilled limit orders like this are allowed to persist, the market maker logic can get a little complicated. As I mentioned, Hanson actually invented an entire class of market makers: Yiling Chen and I have derived the cost and price functions corresponding to the quadratic scoring rule.

It turns out, however, that the quadratic scoring rule market maker is not very interesting or useful in practice. I think it is easy to make an imitation to win the game. I believe that a wonderful market maker should be robust to prevent the users **penoc options trading** play tricks and cheat the market maker to win the game. **Penoc options trading** who are familiar with ordinary financial markets are often the most enthusiastic players in prediction markets, and yes they prefer an interface expressed in terms of quantities to trade.

Glad to see this post, spent a day reading R. The most straightforward way to handle linear outcomes is by breaking up the line into a discrete number of intervals, and then proceeding otherwise as described in the post.

Yiling Chen and I have been working on some other, perhaps more satisfactory, market maker mechanisms for penoc options trading linear markets, which **penoc options trading** hope to report on soon. Because without that information how can we divide the infinite number line into a finite number of finite intervals? Then we need a penoc options trading for incrementing the number of outcomes of the market after the market has been opened, without diminishing the accuracy of the market.

Are you familiar with such a method? This is a great article. Could you also penoc options trading a similar explanation of the paper where Hanson talks about how to integrate the order book with the automated market-maker?

Chris Hibbert tackles the integration problem and it does get complicated. After every transaction, simply randomly cycle through all active limit orders, transacting each with the market maker until the limit is reached or the order is exhausted. Penoc options trading may have to iteratively keep cycling through limit orders until quiesence.

I wrote a more detailed explanation of how to integrate penoc options trading makers and order books. In order to include all the appropriate references, I posted it on my blog. The grossly oversimplified version is that you trade with the market maker up to the price limit imposed by the best book order, then trade with the book order.

Otherwise you repeat those steps in a loop treating each book order as a price limit for trading with the book order, and fully consuming each book order before resuming trade with the AMM.

In the multi-dimensional case, there are multiple book orders that provide constraints, and managing the constraints is more work. But how did you arrive at this result? The easiest way to think about it is to consider the value of the cost function C at the beginning and end of the market.

Given the set of two outcomes: Yet the market maker does not appear to operate this way. The difference is only a matter of accounting and budgeting prior to the realization of the event. After the event happens, all approaches become equivalent. The approach I like best personally is to disallow short selling. Then traders can buy any outcome sand only sell shares of outcomes they already own.

I believe this is the most penoc options trading approach for a wide audience. In the case of multiple states? Can you shed some light on how to cheat the market maker to win the game? Is it by having more penoc options trading one account and then driving the prices up or down? In a play-money market where every new account starts with some amount of cash, you can cheat by opening up penoc options trading accounts and funneling money from your dummy accounts to your main account.

I am new to prediction markets and your explanation is great. I could understand it easily. The best part is that you have explained it using an example with sample calculations.

How about you doing a follow-up post with sample calculations for explaining combatorial markets. How would that be implemented? Thank you very much for this entry. Penoc options trading was very informative. However, I have one question:. I understand how to derive the price function from the cost function penoc options trading vice versa, however, I do not understand how you get any of the two in the first penoc options trading given a particular scoring rule. Perhaps penoc options trading the logarithmic scoring rule as an example?

I cannot understand how to start penoc options trading market where you already know that the responce will tend towards one of the two outcomes.

I would penoc options trading the cost equation to reflect this. Penoc options trading about non binary contracts. There does not seem to be an easy way to derive the cost function for a particular scoring rule, at least that I know of. Yiling Chen and I have derived cost functions for the log and quadractic scoring rules, but each involves a tedious amount of special-case algebra. Yes, that will change increase the maximum possible loss. Yes, LMSR can handle numeric predictions like this as long as the range is discretized into a bunch of intervals.

See penoc options trading example our implementation for Yoopick. Thanks a lot, but discretizing sampling might not suit all applications that well. Anyway, do any of you guys have an idea of what would be the de facto standard market maker algorithm for non binary contracts like the Nokia cell phone price I described above? You could for example discretize down to the nearest penny: Then people can bet on whatever interval they think the Nokia price will fall into.

I have to admit, formulas scare me a little ok, a LOT. But your examples make it a lot easier to get my head around this. Will have to bookmark and come back to another day! Thanks for the detailed penoc options trading. This seems to be the trickiest part in moving toward a continuous version.

If the market maker fills all orders according to a single mathematical rule, then it can never lose money as far as I have been able to test, anyways…. Thanks David, this post helped me a lot. However, I cannot implement your solution to Cost for multiple outcomes. For example, what would the Cost penoc options trading be for a question like the following: See this book chapter for the exact formula: I am writing a research paper on penoc options trading I was wondering if you could spare a few minutes and check out Hubdub, and briefly explain to how their system works.

Have couple of questions: Does it depend on the penoc options trading size i. Does it depend on the initial play money? Too low b and the liquidity is too low. It does depend on the number of players and the amount of play money they penoc options trading. Chris Hibbert suggests having a fairly small b and then integrating an order book together with the market penoc options trading. That may complicate the user interface though. I have problem with its implementation in dynamically changing price markets.

People can bet higher or lower than market price and this is expected to change the market price in return.

David Pennock is one of penoc options trading smartest guys I know. You can learn a lot by watching people vote with their wallets, even without opening your own. Most prediction markets are one-dimensional, which means that every outcome is traded separately.

Combinatorial prediction markets allow traders to buy the full interval in one fell swoop. But combinatorial prediction markets can have an unimaginably large number of outcomes. Think of the red and blue maps that are typically displayed by election pundits. Now think of all the possible configurations of that map that might arise after the election.

Since each of the fifty states can be colored two ways ignoring third partiesin theory there are 2 to the power 50, or 1.

A combinatorial prediction market needs to track each of these possibilities! Of course, this process is an impossibly tedious task no human trader would ever undertake. These combinatoric problems are actually pretty common. To put that number in perspective, there are estimated to be about 10 penoc options trading insects on the planet. So we use an approximation technique to estimate the odds for any prediction a user selects on the fly.

Why do we need or want combinatorial markets? Simply put, they allow us to collect more information. Combinatorial markets reveal the correlations among events like Obama winning both Ohio and Pennsylvaniaand not just their independent likelihoods.

Understanding these correlations is key to many applications, including risk assessment. In fact, many people conjecture the financial crisis was exacerbated due to fundamental underestimation of the possibility of correlated failures. They also translate to financial and betting exchanges, sports bookies, and racetracks. These markets typically treat all outcomes like apples and oranges, processing them independently, even when they are related. In a combinatorial market, a bet on Obama to win Ohio and Penoc options trading automatically affects the market price for that combination, and also for the possibility that he wins the Presidency, as it logically should.

A combinatorial market is a smarter market, letting humans and computers each do what they do best. People enter predictions in simple terms they understand. The computer handles the massive yet methodical number-crunching needed to combine all the pieces together into a coherent overall prediction of a complex event.

Especially in the context of a prediction market, where the goal is to **penoc options trading** information, it makes sense to focus traders on penoc options trading their information, rather than wasting effort on finding and exploiting mispricings between related outcomes. The learning curve in many of these prediction markets is still too steep. First-time traders can get lost in a maze of numbers, jargon, and definitions.

By shifting some penoc options trading that penoc options trading into the central trading pit, the task of traders can, somewhat counter-intuitively, become easier and more natural, leveling the playing field and allowing a wider range of people to participate. And great for information junkies. Interesting, but still prediction markets are not odds any more than futures markets are predictions. For example, I might be long Obama because I want to hedge my tax risk.

Or short because I just want to see analysts use this price as a "prediction". Your right that thin markets might have a very poor signal to noise ratio. And markets where people have a strong emotional reaction to outcomes such as politics and sports are probably noisier than most.

The interesting thing about this work is that it could be a way to thicken the market considerably. Each very specific bet contains information about a multitude of simpler bets that might, or might not, lead to better performance overall. I'm curious, is the point system a zero sum penoc options trading It's not transparent how you make the market liquid for extremely specific bets, but maybe there's a way to make everything work out in the extremely high dimensional space you guys have.

I couldn't find anything about it looking through about 3 layers of info you guys have on it, but please let me know. The California question seems dumb. Obama will win California unless he is replaced by another democrat. Therefore the question should just be will Obama win? Since Democrats have such an entrenched lead in the state. Interestingly, the biggest betting exchange operates single-events bets, multiple event bets which are an "independent" market, but penoc options trading offers multiples bets based on single bets on relatively uncorrelated events which they try to hedge by taking positions on singles markets.

You're right that technically what is revealed is penoc options trading crowd's "risk-neutral" probability. But also long as there are some reasonably deep-pocketed speculators, they can earn an expected profit off of people hedging, so prices should converge toward true probabilities.

The market maker we are using for Predictalot is a positive-sum game: Except we have to approximate it since we can't compute it exactly over 9. What if penoc options trading moderate Republican from California is nominated? He or she might have a shot.

Or other events we can't foresee. There have been some exceptions over the years e. ByThe National Popular Vote bill could guarantee the Presidency to the candidate who receives the most popular votes in all 50 states and DC.

Every vote, everywhere would be politically relevant and equal in presidential elections. Elections wouldn't be about winning penoc options trading. Every vote, everywhere would be counted for and directly assist the candidate for whom it was cast. Candidates would need to care about voters across the nation, not just undecided voters in a handful of swing states.

In the penoc options trading, pundits and campaign operatives already agree that only 14 states and their voters will matter under the current winner-take-all laws i. Candidates have no reason to poll, visit, advertise, organize, campaign, or care about the voter concerns in the dozens of states where they are safely ahead or hopelessly behind.

The bill would take effect only when enacted, in identical form, by states possessing a majority of the electoral votes--enough electoral votes to elect a President of When the bill comes into effect, all the electoral votes from those states would be awarded to the presidential candidate who receives the most popular votes in all 50 states and DC.

The bill uses the power given to each state by the Founding Fathers in penoc options trading Constitution to change how they award their electoral votes for president. Historically, virtually all of the major changes in the method of electing the President, including ending the requirement that only men who owned substantial property could vote and 48 current state-by-state winner-take-all laws, have come about by state legislative action.

Support for a penoc options trading popular vote is strong in virtually every state, partisan, and demographic group surveyed in penoc options trading polls in closely divided battleground states: I like this idea and had heard of it but didn't realize it had penoc options trading so far -- thanks. I was going to ask what is **penoc options trading** for the ground truth measurement of the "most popular votes in all 50 states and DC ", but I see it and almost any other question one can think of is answered on the website: Yes, you're right Kevin.

We only modeled the "core 64" after the first four play-in games. Stephen Dubner's conversation with the Facebook founder and C. Season 7, Episode 30 Only 5 percent of Fortune companies are run **penoc options trading** women. Research shows that female executives are more likely to be put in Stephen Dubner's conversation with the former C. Not so fast on assuming the presidential election results can be predicted as usual. Beer or Wine as Proof?