1. You are given the following information: The current gold price is $1,870, the net convenience yield for gold is 1.7% per year, the risk-free rate is 3% per year, the volatility is 20% per year, the expected return is 0% per year, and based on the anticipated skewness, the true probability of the high state is 0.8.

a) Build a 2-period binomial model for the (6-month) spot price of gold over one year.

b) A financial engineering firm is developing a new derivative they're calling a "Golden Square." The payoff of the derivative is the spot price of gold squared (V_T = S_T²). Use the binomial model from part a) to estimate the value of a golden square maturing in one year using the tracking portfolio approach.

c) Use the binomial model from part a) to estimate the value of a golden square maturing in one year using the backward induction risk-neutral valuation approach.

d) Use the binomial model from part a) to estimate the value of a golden square maturing in one year using the direct risk-neutral valuation approach.