Gold Mine Example

Overview


This example is simple demonstration of real options analysis. In this example, you have a lease that allows you to extract goal from a mine in a given year, or to leave it dormant.

The price of gold is a random quantity. At the beginning of each year, you can lock in the current price of gold for the gold you extract. It costs you $100 to extract the gold.

For simplicity, we assume that the gold price follows a binomial tree. We will assume that the price of gold starts at $100. Your option to lease the mine extends over 5 periods, and the question is how much is the lease worth.

Binomial Tree


Next we construct the binomial tree using the computed parameters.



The following code computes the value of the gold mine lease. 


let r = 0.05;
let u = 1.1;
let d = 1/1.1;
let t = 1;
let prob = (Math.exp(r*t) - d)/ (u-d);

//construct a 5 period binomial tree starting a 100 with the given parameters.
let tree = bt.binomial(100, 5, u, d, prob);

let value = 0;
for(let i=1;i<tree.length;i++){
    let layer = tree[i];
    let sum = 0;
    for(let item of layer){
        sum += item.probability * Math.max(0, item.value - 100);			
    }
    //discount the value back
    value += Math.exp(-1*r*i) * sum;
}
Try it!

Contents