A class of Health-Jarrow-Morton models in which the unbiased expectations hypothesis holds

The unbiased expectations hypothesis states that forward rates are unbiased estimates for future short rates. Cox, Ingersoll and Ross [1] conjectured that this hypothesis should be inconsistent with the absence of arbitrage possibilities. Using the framework of Heath, Jarrow and Morton [4] we show that this is not always the case. The unbiased expectations hypothesis together with the existence of an equivalent martingale measure is equivalent to a certain condition on the volatilities of the forward rates.