Suppose that you own a piece of property in New Territories, and similar parcels of land near yours have sold recently for $10 million. A developer has approached you and asked you for a one-year option to purchase the property at the prespecied price of $12.5 million. The required rate of return on land, , is 10% per year and the standard deviation of log returns on land, , is 25% per year. The expected log return on land, m, is 6.875% per year. The riskless rate of interest, r, is 5% per year. All compounding and discounting are done in continuous time.

(a) Build a 6-step binomial tree by using the multiplier for an up step equal to U = e t and that for a down step equal to D = e t , where t is the length of time for each binomial time step.

(b) Use the formula that the subjective probability of an up step is equal to