Kangaroo inc is a U. S. company whose shares are listed on and freely traded on the New York stock exchange. Let St be the price of Kangaroo inc shares in dollars, at time t (measured in years). Time zero is today.
You are (still) the Global Head of Equity Options trading at Goldman Sachs. You are approached by a hedge fund that today wants to buy a security (called a SQUARED DIFFERENCE contract) that has the following features:
The SQUARED DIFFERENCE security has a maturity of one year.
At maturity, the SQUARED DIFFERENCE security pays an amount in dollars equal to the amount:
(S1)^2 - (S0)^2 / (S0)^2
Here, S1 and S0 are, respectively, the Kangaroo inc share price one year from now and the share price today.
Assume that the risk-free interest rate is zero per cent and that Kangaroo inc shares pay no dividends. Assume that the share price, in dollars, today is S0 = 1.
a) Using Excel, build a four-step binomial tree (this means each time step corresponds to three months).