The current price of gold is $400. The risk-free rate is 10% and the annual volatility for….
The current price of gold is $400. The risk-free rate is 10% and the annual volatility for changes in gold prices is 30%. Gold prices are assumed to follow a lognormal distribution. Each year the mine is open a fixed cost of $1 million is incurred. This cost is incurred even if no gold is mined during the year. If we open (or re-open) the mine a cost of $2 million is incurred. If we shut the mine a fixed cost of $1.5 million is incurred. During the current year and each of the next 15 years we can, if the mine is open, mine up to 10,000 ounces of gold at a variable cost of $250 per ounce. What is the worth of this situation? Assume the mine is open at the beginning of year 1. Hint: One way to solve this problem is to approximate the log-normal distribution by a binomial lattice, and then formulate the problem as a dynamic program. Think carefully about what the state would be if you try the dynamic programming approach. You are also welcome to try other approaches.
The current price of gold is $400. The risk-free rate is 10% and the annual volatility for…
