A bank has $20M face value of a certain bond. The current price of these bonds are 0.90 (thus the value of this position is currently $18M), and the duration of these bonds is 3. Suppose that the bank bought puts on $15M FV worth of these same bonds, each with a strike price of 0.90. If the value of the bonds stay the same, what is the value of the options at expiration? If the interest rate factor increased by 2% marketwide, what would the new value of these bonds be? If the options were expiring at this point, what is the value of the options? What would the combined value of the options and the bond position be?