Looking at historical options and stock price data in conjunction, I've noticed that puts are systematically cheaper than calls, e.g. in the money puts are cheaper than out of the money calls, which does not make sense. My impression is that, for some reason, historical stock prices are lower than their actual values. That appears to be the case at least for SPY, where I compared it with the data I get from my broker, and it also appears to be the case for IBM.

In the last row of the table below, strike > stock, meaning put is in the money, and call is out of the money, and yet the put price is lower than call price.

      dateexpirystrikestockcallputdays to maturity2018-01-022018-12-21257.0259.62471122.425010.1100352.02018-01-022018-12-21258.0259.62471121.700010.3750352.02018-01-022018-12-21259.0259.62471120.955010.6450352.02018-01-022018-12-21260.0259.62471120.245010.9250352.02018-01-022018-12-21261.0259.62471119.545011.2150352.02018-01-022018-12-21262.0259.62471118.845011.5100352.0

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