# The following analysis comes from the intrade presidential election data.  The futures return \$100 if the candidate wins.  Stable parameters for the 180 day data.

 α β γ δ Obama Closing 1.34382 0.251771 0.0110979 0.00479108 McCain Closing 1.35626 -0.0702056 0.0197488 -0.00511718

Here are some calculations.  They are made using the assumption that the data are stably distributed with the above calculated parameters.  The distribution of most recent 180 days of logarithmic returns is scaled to a distribution that would account for the sum of returns for all the days remaining until the election.  Since the returns are differences, scaling magnifies the trend in the data and will not be very accurate until we are much closer to the election.  The numbers may not add to one because they are calculated from different data sets.  The McCain probability is calculated from the return from the last price to a price of 50 on November 4, from the McCain closing price data.  The Obama probability is calculated likewise from the Obama data.  Keep in mind that the scaling of stable distributions is linear with respect to the expectation or the δ parameter; since the δ parameter is the mean logarithmic change, this analysis is influenced markedly by the dominant trend in the period selected, as the number of days until the election decreases this effect will diminish.

Data scaled by 1 days.  Last data point on Mon 3 Nov 2008.

Probability of McCain win in November 0.000682342

Probability of Obama win in November 0.99909

Here are similar calculations based on a sample of only the last 90 days.

 α β γ δ Obama Closing 1.50529 0.375451 0.0126377 0.00611044 McCain Closing 1.52575 -0.339677 0.0309098 -0.0145821

Probability of McCain win in November 0.000368312

Probability of Obama win in November 0.999605

There are some problems with the prediction market price model, first, prices have an practical upper limit of 100.  Second we see that the parameters of our two distributions are quite different and the probabilities don't come close to adding to 1.  We present a more sophistocated approach to analysis on our Presidential Prediction page. 