A European call option is a type of financial derivative contract that provides the right (but not the obligation) to purchase an asset at a fixed price K at a future time T . If the asset’s price at...

A European call option is a type of financial derivative contract that provides the right (but not the obligation) to purchase an asset at a fixed price K at a future time T . If the asset’s price at time time t is given by a price process St , then, under a complete and perfect assumption, the value (or premium) of the call option at time 0 is given as C0 = e−rf TE Q[(ST −K)+] , where rf is the riskfree rate (earned by a riskless zero-coupon bond that pays no interest until time T when it matures and pays a face value of one with certainty) and Q is a measure over ω known as the equivalent martingale measure. While it is common to assume ST under Q has a log-normal distribution, the distribution is often unknown. The bounds in this section can be used if only partial information is given. Suppose that only the mean and variance of ST under Q is known. Show that the call function satisfies the conditions for a two-point support and find the maximum price that is consistent with these moments as a function of the mean, variance, and K . (Note that ST ≥ 0 as well.) (Lo [1987].)