Assume today is Sept 1, 2021. Company IMineGold is a gold mining company producing gold with plans to increase its size and valuation over the next few years. The company has invested in developing goldfields and commenced extracting gold and gold production from its underground mines. The company is confident that it will have an output of 100,000 ounces of gold on 1 March 2022 and is willing to sell this output amount on that day.

Following further information is available:

Profit margin is defined as (Revenue Cost of Goods Sold) / Revenue.

The cost of mining one ounce of gold is $1,420. The company has a target profit margin of 18%.

The minimum acceptable profit margin below which the company will have difficulties servicing its debt is 14%.

The spot price of gold on 1 Sept 2021 is $1,800.

The interest rate curve is flat and the risk-free interest rate for all maturities is 2% (cont. comp.).

Use the Black-Scholes model to price following options on gold:

Option 1: A call option with strike price 1680 expiring on 1 March 2022.

Option 2: A put option with strike price 1680 expiring on 1 March 2022.

Option 3: A call option with strike price 1850 expiring on 1 March 2022.

Option 4: A put option with strike price 1850 exp

The annual gold price volatility is estimated to be 15%.