You are the risk manager at a bank. The bank is considering two options for its operations. These are:

Option $1$: $$150$ million in liabilities with an average duration of $3$ years, $$175$ million in assets with an average duration of $6$ years.

Option $2$: $$150$ million in liabilities with an average duration of $4$ years, $$175$ million in assets with an average duration of $2$ years.

Further suppose that you expect interest rates to increase from $2\%$ to $6\%$ over the next several years. Based on this, which option should the bank pursue? Perform a duration analysis for each option, and describe carefully what would happen if interest rates do increase.