(1) Ê[S

_{T}] = Se

^{rT}

It states that the expected value 'in a risk neutral world' of the price of a non-income paying asset at time T is equal to the current (i.e. time = 0) asset price compounded at the risk free rate r. The assumption is clearly equivalent to the claim that there is no risk premium: that

*on average*the price of the asset will grow at the risk free rate.

The claim is true, but only in a 'risk neutral world', i.e. a world where there is no risk premium. Otherwise it is false. Why do people think it is generally true? I have looked at many presentations and discussions of the assumption, and they all start with the following assumption

(2) F = Se

^{rT}

This says that the price F we would

*rationally*agree

*now*, to pay for the asset

*at T*, is equal to the current asset price compounded at risk free. That is clearly true, given the 'rationally'. If I agree a price now, I take on the price risk from the seller. But the seller receives no money until T. So the seller will charge interest at a rate r. Call this the no-arbitrage/rational pricing assumption.

However (2) is not equivalent to (1). Why then do people think that we can derive (1) from (2)? Or perhaps we can? How?