At time t = 0, a speculator acquires a European call option with strike price xs and finite expiration time τ. Thus, the option can only be exercised at time τ at price xs, independently of its market...

At time t = 0, a speculator acquires a European call option with strike price xs and finite expiration time τ. Thus, the option can only be exercised at time τ at price xs, independently of its market value at time τ. The price X(t) of the underlying risky security at time t is

Where {D(t), t ≥ 0} is the Brownian motion with positive drift parameter and vola- tility σ²
If X(τ) > xs , the speculator will exercise the option. Otherwise, he will not. As in example 7.16 assume that

1) What will be the mean undiscounted payoff of the speculator (cost of acquiring the option not included)?

2) Under otherwise the same assumptions, what is the investor's mean undiscounted profit if