It's one question.

Consider a bank with the following balance sheet: 150 of 5 years maturity bullet debt paying, every year, 12 months market rate prevailing at payment date +0,50% floored at 0,50%. Last payment just performed today. Volume of 100 of savings accounts with client rate at 0,1% Volume of 200 of non-remunerated deposits 50 of own funds 100 of 2 years maturity fixed rate bond coupon equal to 1,5% 400 of 4 years maturity floating rate bullet loan with client rate equal to 6 months market rate +1% with semestral interest rate payments, last fixing occurred 3 months ago. The bank has also entered a 1 year forward payer interest rate swap 1% fixed rate against 3 months market rate for a notional of 100, duration 2 years, maturity 3 years. Let us assume that the volume of non-remunerated deposits can be projected as the product between the average amount per (100 if t s 3 years account A(t) and the number of accounts N(t) with A(t) = 2 and N(t) = ( 80 if t > 3 years and that the projected volume of savings is constant. Let us assume that the replicating portfolio of the savings is 70% 1 year linear and 30% 5 years linear. Let us assume that the target linear investment profile of non-remunerated deposits is 100% 3 months linear and that the target linear investment profile of the own funds is 100% 4 years linear. Let us assume that there are only 3 equiprobable scenarios of possible evolution of market interest rates: Scenario 1 1Y horizon 2Y horizon 3Y horizon 48 horizon 5Y horizon 3M rate -0,75% -0,65% -0,55% -0,45% -0,35% 6M rate -0,50% -0,40% -0,30% -0,20% -0,10% 12M rate -0,25% -0,15% -0,05% 0,05% -0,05% Scenario 2 3M rate 6M rate 12M rate 1Y horizon -0,60% -0,40% -0,15% 2Y horizon -0,50% -0,30% -0,05% 3Y horizon -0,25% -0,10% 0,25% 48 horizon -0,15% 0,05% 0,30% 5Y horizon 0,00% 0,20% 0,45% Scenario 3 3M rate 6M rate 12M rate 19 horizon -0,30% -0,10% 0,05% 2Y horizon -0,25% -0,05% 0,10% 3Y horizon -0,20% 0,00% 0,15% 48 horizon -0, 15% 0,05% 0,20% 5Y horizon -0,10% 0,10% 0,25% Compute the contribution of each balance sheet item as well as of the forward swap to the cumulated fixed interest rate gap and to the liquidity gap and deduce the cumulated fixed interest rate gap and the liquidity gap of the bank up to an horizon of 10 years (you can use millimeter sheet or compute graphics in excel e.g.). Detail your computations as much as possible and respect the conventions defined in the course. Based on the gaps obtained, compute the Net Interest Income variation ANII]12M; 13M] over the 13th month of projection in case of a 10 bps downwards shock affecting all floating interest rates and explain whether the computed figure is exact or is an approximation and why. Detail your computation as much as possible. Consider a bank with the following balance sheet: 150 of 5 years maturity bullet debt paying, every year, 12 months market rate prevailing at payment date +0,50% floored at 0,50%. Last payment just performed today. Volume of 100 of savings accounts with client rate at 0,1% Volume of 200 of non-remunerated deposits 50 of own funds 100 of 2 years maturity fixed rate bond coupon equal to 1,5% 400 of 4 years maturity floating rate bullet loan with client rate equal to 6 months market rate +1% with semestral interest rate payments, last fixing occurred 3 months ago. The bank has also entered a 1 year forward payer interest rate swap 1% fixed rate against 3 months market rate for a notional of 100, duration 2 years, maturity 3 years. Let us assume that the volume of non-remunerated deposits can be projected as the product between the average amount per (100 if t s 3 years account A(t) and the number of accounts N(t) with A(t) = 2 and N(t) = ( 80 if t > 3 years and that the projected volume of savings is constant. Let us assume that the replicating portfolio of the savings is 70% 1 year linear and 30% 5 years linear. Let us assume that the target linear investment profile of non-remunerated deposits is 100% 3 months linear and that the target linear investment profile of the own funds is 100% 4 years linear. Let us assume that there are only 3 equiprobable scenarios of possible evolution of market interest rates: Scenario 1 1Y horizon 2Y horizon 3Y horizon 48 horizon 5Y horizon 3M rate -0,75% -0,65% -0,55% -0,45% -0,35% 6M rate -0,50% -0,40% -0,30% -0,20% -0,10% 12M rate -0,25% -0,15% -0,05% 0,05% -0,05% Scenario 2 3M rate 6M rate 12M rate 1Y horizon -0,60% -0,40% -0,15% 2Y horizon -0,50% -0,30% -0,05% 3Y horizon -0,25% -0,10% 0,25% 48 horizon -0,15% 0,05% 0,30% 5Y horizon 0,00% 0,20% 0,45% Scenario 3 3M rate 6M rate 12M rate 19 horizon -0,30% -0,10% 0,05% 2Y horizon -0,25% -0,05% 0,10% 3Y horizon -0,20% 0,00% 0,15% 48 horizon -0, 15% 0,05% 0,20% 5Y horizon -0,10% 0,10% 0,25% Compute the contribution of each balance sheet item as well as of the forward swap to the cumulated fixed interest rate gap and to the liquidity gap and deduce the cumulated fixed interest rate gap and the liquidity gap of the bank up to an horizon of 10 years (you can use millimeter sheet or compute graphics in excel e.g.). Detail your computations as much as possible and respect the conventions defined in the course. Based on the gaps obtained, compute the Net Interest Income variation ANII]12M; 13M] over the 13th month of projection in case of a 10 bps downwards shock affecting all floating interest rates and explain whether the computed figure is exact or is an approximation and why. Detail your computation as much as possible