A stock is currently priced at $25. We model the possible movement of stock price over the next 3 months using a one-step Binomial tree. This means that u = 1.2214 and d = 0.8187. The riskfree rate of interest is 5% pa continuously compounded.

Let ST denote the stock price 3 months from now. Define a new derivative security which has a payoff equal to $1000/ST. That is, if you buy this derivative security today, in 3 months time, you will receive a cash payment equal to $1000 divided b6y whatever the stock price is at the point.

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