The fallacy is very clearly articulated here.
The author correctly states that “the historical evidence can soundly reject the hypothesis that the expected rate of house price inflation is equal to the risk free rate,” then incorrectly states that “the Black Scholes priced put option gives you that expected value if and only if the expected value of house price inflation equals the risk free rate”.
Kevin and I address the fallacy in a forthcoming paper, but I will briefly discuss it here.