In a 3-month down-and-out call option on silver futures the strike price is $20 per ounce and the barrier is $18. The current futures price is $19, the risk-free interest rate is 5%, and the volatility of silver futures is 40% per annum.
Explain how the option works and calculate its value.
What is the value of a regular call option on silver futures with the same terms?
What is the value of a down-and-in call option on silver futures with the same terms?