A bank has 20 coupon-bonds, each with a face-value of $1M. The current value of this position is $18M, and the duration of these bonds is 3.

Suppose that the bank bought 15 puts on these coupon bonds, each with a strike price of $900,000.

If the value of the bonds stay the same, what is the value of the options at expiration?

If interest rates increase by 2%, what would the new value of these bonds be?

What would the value of one option be at expiration?

What would the combined value of the options and the bond position be?