PROBLEM 12-4: Valuation an American Option Given Risk-neutral probability Risk free Interest rate Discount factor = exp(Risk free interest rate)...

J&B Drilling Company has recently acquired a lease to drill for natural gas in a remote region of southwest Louisiana and southeast Texas. The area has long been known for oil and gas production, and the company is optimistic about the prospects of the lease. The lease contract has a three-year life and allows J&B to begin exploration at any time up until the end of the three-year term. J&B’s engineers have estimated the volume of natural gas they hope to extract from the leasehold and have placed a value of $25 million on it, on the condition that explorations begin immediately. The cost of developing the property is estimated to be $23 million (regardless of when the property is developed is developed over the next three years). Bases on historical volatilities in the returns of similar investments and other relevant information, J&B’s analysts have estimated that the value of the investment opportunity will evolve over the next three years.