Assessing the Value of a Stock Special Deal: Black-Scholes Equation Analysis

[squenshl]

Homework Statement

Assume a stock currently has a price S(0) = 1 in dollars units. As a special deal, you may purchase this stock at this price but you sell this stock at a specified time t = T (at the maturity) at the selling price S(T)². For example, if at the maturity S(T) = 0.5, you will sell it at the price 0.25. Is this a good deal? Give reason(s).

Homework Equations

Black-Scholes equation.

The Attempt at a Solution

I solved the Black-Scholes equation when r = 0 so I solve V_t + sigma^2*S^2/2*V_ss = 0 with inital condition ((S(T)-K)⁺)² and got V(S,t) = e^{sigma^2(T-t)}*S(T)^2. How can I tell if this is a good deal? Help please.

 

[spamiam]

I'm by no means an expert, but often we use expectation to see if something is a "good deal" or not. If the expected selling price is greater than the cost, it would be a good deal.

 

[squenshl]

My lecturer told me to solve this but the only problem is that I don't know how to interpret it.