### Discounting and prediction market prices

The prolific Alex Forshaw asks why 2008.GOP.NOM.HUCKABEE trades above 7. But should you sell even an

Discounting returns may not bias prices for a number of reasons, including de-biasing by large interest-earning accounts, a short average trade horizon, and gamblers' "irrationality". Insofar as rates (and commissions) are found to affect prediction market prices, then perhaps an "implied probability" or "delta" metric to supplement price is inevitable. In that case, if we interpret price as probability, then the price will be biased, but only because of our interpretation.

*impossible*event for less than 100-(100/((1+(r-r_{m}))^T)+ c? Here, T is the years to expiration, r the risk-free rate, r_{m}the yield on your margin (which is zero for most Intrade traders), and c is the trading fee, which is currently less than or equal to 0.5 + 1/(1+r)^T (a 0.5% price-taker's entry fee plus the present value of the 1% in-the-money fee). The price of 2008.GOP.NOM.HUCKABEE seems more reasonable with this is mind, but traders are only interested in selling the whole set of possibilities for more than 100*(1+(r-r_{m}))^T + Σc, or buying them for less than 100/(1+(r-r_{m}))^T - Σc. This will mitigate any discounting "bias". (Play-money markets also have a discount rate, but it is logically and empirically much less. Play-money markets also show some evidence of yield curve inversion.)Discounting returns may not bias prices for a number of reasons, including de-biasing by large interest-earning accounts, a short average trade horizon, and gamblers' "irrationality". Insofar as rates (and commissions) are found to affect prediction market prices, then perhaps an "implied probability" or "delta" metric to supplement price is inevitable. In that case, if we interpret price as probability, then the price will be biased, but only because of our interpretation.

## 3 Comments:

Reminds me of the "quasi arbitrage" discussion in an options class I took. Transaction costs precluded an S&P futures - cash arbitrage but the presumption was that a bunch of people buying the cheaper instrument would encourage the alignment of prices, just less forcefully than textbook arbitrage would prefer. And a small band of mispricing could persist for a while.

In this election market expiry is a couple years away. There are transaction costs (e.g. TradeSports lowballing the interest payment on margin) associated with a long-dated position and often no near-term catalyst to suggest the price will change favorably in the short-term. It wouldn't be surprising if dark horses have odds too rich. Academics would stick the term "risk premium" on it.

By john d, at 5:25 PM

The problem with this is PUT/Call parity..

The probability of Candidate x winning is of course the 1-the probability of him losing..

So your arguement would imply that the Put too would bear a risk premium..

Risk premium of winning, risk premium of losing..

Better word: fudge factor..

By stan.jonas@gmail.com, at 9:24 AM

Thanks for these comments.

Since we stipulated an impossible event here, the only inputs to the discount rate are the expected risk free rate and rate the trader is making on his 100% margin. No additional risk premium is involved.

What my example illustrates is perhaps mainly the immaturity of these markets, in which accounts typically do not earn interest.

It would also be desirable to have an explicit not-X contract in situations with many possibilities. Otherwise trading all non Xs could be made infeasible by commissions, which act as friction to put-call parity.

By Jason Ruspini, at 12:55 PM

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