A stock is currently priced at $20. We model the possible movement of stock price over the next 3 months using a one-step Binomial tree. This means that u = 1.1618 and d = 0.8607. The riskfree rate of interest is 8% pa continuously compounded.

Let ST denote the stock price 3 months from now. Define a new derivative security which has a payoff equal to. That is, if you buy this derivative security today, in 3 months' time, you will receive a cash payment equal to whatever the finishing share price is, to the power of three.

What is the fair price to pay for this derivative security in the market today?