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 S_T 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?

Enter your answer to 2 decimal places. Do not enter a dollar sign in your answer.