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.
We price the option off the current price of a forward contract. Note ‘current price’, not ‘future price’. A forward contract is a contract to acquire an income producing asset at some future date (the deferment date), at a price agreed now, but to be settled (i.e. paid) at the deferment date. The forward contract is in turn priced off a deferment contract, where we still acquire the income producing asset at the deferment date, but we pay (money changes hands) now, rather than later.
It follows that the value of deferred possession equals the value of immediate possession minus the present value of lost income, hence the difference between the price of the forward contract and the deferment contract reflects the interest lost only, given that the seller of both types of contract passes on the price risk to the buyer now, but with no immediate payment in the case of the forward.
Once you see that the forward contract has a price now, which is continually changing in near lockstep with the price of the deferment contract and the asset itself, and once you see that the price of all three instruments converges at the deferment date, you are less tempted to think of the forward price as a kind of prediction of the future asset price. Of course not. How could the price of the forward contract, which will in the future converge with the asset price, predict its own future path?
So, pricing the option off the forward does not involve any kind of prediction of future asset prices, and it is entirely false to suppose 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”. Option pricing (and forward and deferment contract pricing) has absolutely nothing to do with predicting the future.