Annex III – The standardised interest rate shock scenarios

The six interest rate shock scenarios for measuring EVE under the standard EVE outlier test are:

• (i) parallel shock up;
• (ii) parallel shock down;
• (iii) steepener shock (short rates down and long rates up);
• (iv) flattener shock (short rates up and long rates down);
• (v) short rates shock up; and
• (vi) short rates shock down.

Institutions should apply the six above-mentioned interest rate shock scenarios to capture parallel and non-parallel gap risks for EVE. These scenarios are applied to IRRBB exposures in each currency separately for which the institution has material positions¹⁷ .

The shock size for the six interest rate shock scenarios is based on historical interest rates. More precisely, for capturing the local interest rate environment and cycle, a historical time series ranging from 2000 to 2015¹⁸ for various maturities is used to calculate the parallel, short-end (‘short’) and long-end (‘long’) shocks for a given currency. However, deviations from the above-mentioned 16-year period are permitted if they better reflect a particular jurisdiction’s idiosyncratic circumstances.

Table 1 displays the values calculated for the parallel, short and long interest rate shocks for selected currencies. The shocks capture the heterogeneous economic environments across the jurisdictions. These are then used to calculate the shocks for different maturities of the yield curve to create the interest rate shock scenarios as per the methodology explained below.

Table 1. Specified size of interest rate shocks

ARS AUD BRL CAD R � CHF shocktype CNY , c EUR GBP HKD IDR INR Parallel 400 300 400 200 100 250 200 250 200 400 400 Short 500 450 500 300 150 300 250 300 250 500 500 Long 300 200 300 150 100 150 100 150 100 350 300

JPY KRW MXN RUB SAR SEK SGD TRY USD ZAR Parallel 100 300 400 400 200 200 150 400 200 400 Short 100 400 500 500 300 300 200 500 300 500 Long 100 200 300 300 150 150 100 300 150 300

¹⁷ Material positions are defined in section 4.5, ‘Supervisory outlier test’.

¹⁸ The EBA may envisage a recalibration in due course.

For calibrating interest rate shock sizes for further currencies, the following proceeding shall be applied:

Step 1: Calculation of the daily average interest rate

Collect a 16-year time series of daily ‘risk-free’ interest rates for each currency for the maturities 3M, 6M, 1Y, 2Y, 5Y, 7Y, 10Y, 15Y and 20Y. Then, calculate the overall average interest rate for each currency across all observations in the time series and for all maturities. The 𝑐𝑐 result is a single measure per currency. 𝑐𝑐 Step 2: Applying the global shock parameters

Apply the global shock parameters on the average interest rate, as per Table 2 below, to each currency .

Table 2. 𝑐𝑐 Baseline global interest rate shock parameters

Parallel 60%

Short 𝛼𝛼� 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 85%

Long 𝛼𝛼� 𝑠𝑠ℎ𝑜𝑜𝑝𝑝𝑜𝑜 40%

𝛼𝛼� 𝑝𝑝𝑜𝑜𝑙𝑙𝑙𝑙 Applying the global shock parameters from Table 2 to the average interest rates calculated in step 1 results in revised interest rate shocks by currency for the different segments of the yield curve, i.e. for the parallel, short and long shocks.

Step 3: Applying the caps and floors

The proposed interest rate shock calibration can lead to unrealistically low interest rate shocks for some currencies and to unrealistically high interest rate shocks for others. In order to ensure a minimum level of prudence and a level playing field, a floor of 100 bps as well as variable caps (denoted as are set as 500 bps for the short-term shock, 400 bps for the parallel shock and 300 bps ∆𝑅𝑅 for � 𝑗𝑗 the ( 𝑡𝑡 𝑘𝑘 )) long-term shock, respectively.

The change in the ‘risk-free’ interest rate for shock scenario j and currency , at time bucket tenor midpoint can be defined as: 𝑐𝑐 𝑡𝑡 𝑘𝑘¹⁹

where �∆𝑅𝑅� , for 𝑗𝑗 , 𝑐𝑐 ( j 𝑡𝑡 = 𝑘𝑘 ) { parallel � = max , short � 100,min and long � | ∆𝑅𝑅 }, 𝑗𝑗 , 𝑐𝑐 respectively. ( 𝑡𝑡 𝑘𝑘 )|, ∆𝑅𝑅� 𝑗𝑗 �� , Applying the caps and of floors interest to ∆𝑅𝑅� the 𝑗𝑗 rate = shocks {400,500,300} shocks calculated by currency in step as shown 2, and rounding in Table 1. to the nearest 50 bps, results in the final set

Step 4: Adjustments for further currencies that are not shown in Table 1

As jurisdictions might have experienced major economic changes within the period 2000 to 2015, the proceeding in steps 1 to 4 might not be adequate for some of them. This is particularly the case if the interest rates during the first years of the period differ considerably from the interest rates in the more recent years. For currencies that are not mentioned in Table 1, the time series to be used to calculate the average interest rate as per step 1 is determined using the following principle: If the average interest rate calculated as per step 1 for the period 2000 to 2006 is greater than 700 bps, then data from the most recent 10 years (i.e. 2007 to 2016) or until when data is available shall be used; otherwise the full time series of data from 2000 to 2015 shall be used.

Using this principle allows us to identify high interest rate environments and periods of significant structural change before the financial crisis. Further, this principle aims at finding those currencies that exceed the cap (700 bps 0.6 = 420 bps > 400 bps) in the first years of the period considered and fosters a stronger consideration of more recent observed interest rates. ⋅ Table 3 shows the results of applying steps 1 to 4 on EU currencies that are not covered in Table 1. Interest rate shock sizes for other currencies can be similarly retrieved by applying the methodology outlined in this section.

Table 3. Specified size of interest rate shocks for additional EU currencies R � shocktype , c

BGN CZK DKK HRK HUF PLN RON Parallel 250 200 200 250 300 250 350 Short 350 250 250 400 450 350 500 Long 150 100 150 200 200 150 250

¹⁹ In the case of rotation shock scenarios, cannot exceed 500 bps, and cannot exceed 300 bps, whereby denotes the time bucket with the lowest maturity and the time bucket with the highest maturity. ∆𝑅𝑅� 𝑗𝑗 , 𝑐𝑐 ( 𝑡𝑡 1 ) ∆𝑅𝑅� 𝑗𝑗 , 𝑐𝑐 ( 𝑡𝑡 𝐾𝐾 ) 𝑡𝑡 1 𝑡𝑡 𝐾𝐾 50

Given for each currency c the specified size of the parallel, short and long instantaneous shocks to the ‘risk-free’ interest rate, the following parameterisations of the six interest rate shock scenarios should be applied:

• (i) Parallel shock for currency c : A constant parallel shock up or down across all time buckets:
• (ii) Short rate shock for currency ∆𝑅𝑅 c : 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 Shock , up 𝑐𝑐 ( 𝑡𝑡 𝑘𝑘 or )= down ± 𝑅𝑅 � 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 that is greatest , 𝑐𝑐 at the shortest tenor

midpoint. That shock, through the shaping scalar −𝑡𝑡 k , where , diminishes toward zero at the tenor of the longest point on the term structure 𝑥𝑥²⁰ . Where t k is the midpoint (in time) of the k th bucket and t K is the midpoint 𝑆𝑆 𝑠𝑠ℎ𝑜𝑜𝑜𝑜𝑡𝑡 ( 𝑡𝑡 𝑘𝑘 (in ) = time) 𝑒𝑒 of the last 𝑥𝑥 bucket = 4

):

𝐾𝐾 k

• (iii) Long rate shock ∆𝑅𝑅 𝑠𝑠ℎ𝑜𝑜𝑝𝑝𝑜𝑜 for , 𝑐𝑐 currency ( 𝑡𝑡 𝑘𝑘 )= ± c : 𝑅𝑅� This 𝑠𝑠ℎ𝑜𝑜𝑝𝑝𝑜𝑜 shock , 𝑐𝑐 ∙ 𝑆𝑆 𝑠𝑠ℎ𝑜𝑜𝑝𝑝𝑜𝑜 is only ( 𝑡𝑡 𝑘𝑘 applied )= ± 𝑅𝑅� to 𝑠𝑠ℎ𝑜𝑜𝑝𝑝𝑜𝑜 rotational , 𝑐𝑐 ∙𝑒𝑒 𝑥𝑥 shocks. The shock is greatest at the longest tenor midpoint and is related to the short scaling factor as :

𝑆𝑆 𝑙𝑙𝑜𝑜𝑙𝑙𝑙𝑙 ( 𝑡𝑡 𝑘𝑘 ) = 1 − 𝑆𝑆 𝑠𝑠ℎ𝑜𝑜𝑜𝑜𝑡𝑡 ( 𝑡𝑡 𝑘𝑘 ) k

• (iv) Rotation shocks ∆𝑅𝑅 𝑝𝑝𝑜𝑜𝑙𝑙𝑙𝑙 for , 𝑐𝑐 ( 𝑡𝑡 currency 𝑘𝑘 )= ± 𝑅𝑅� c 𝑝𝑝𝑜𝑜𝑙𝑙𝑙𝑙 : Involving , 𝑐𝑐 ∙ 𝑆𝑆 𝑝𝑝𝑜𝑜𝑙𝑙𝑙𝑙 rotations ( 𝑡𝑡 𝑘𝑘 )= ± to 𝑅𝑅� the 𝑝𝑝𝑜𝑜𝑙𝑙𝑙𝑙 term , 𝑐𝑐 ∙� structure 1 −𝑒𝑒 𝑥𝑥 � (i.e. for steepeners

and flatteners ) of the interest rates, whereby both the long and short rates are shocked and the shift in interest rates at each tenor midpoint is obtained by applying the following formulas to those shocks:

∆𝑅𝑅 𝑠𝑠𝑜𝑜𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝 , 𝑐𝑐 ( 𝑡𝑡 𝑘𝑘 ) = − 0.65 ∙ ∣ ∆𝑅𝑅 𝑠𝑠ℎ𝑜𝑜𝑝𝑝𝑜𝑜 , 𝑐𝑐 ( 𝑡𝑡 𝑘𝑘 ) ∣ +0.9 ∙ ∣ ∆𝑅𝑅 𝑝𝑝𝑜𝑜𝑙𝑙𝑙𝑙 , 𝑐𝑐 ( 𝑡𝑡 𝑘𝑘 ) ∣ Examples: ∆𝑅𝑅 𝑓𝑓𝑝𝑝𝑝𝑝𝑜𝑜𝑜𝑜𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝 , 𝑐𝑐 ( 𝑡𝑡 𝑘𝑘 )= +0.8 ∙ ∣ ∆𝑅𝑅 𝑠𝑠ℎ𝑜𝑜𝑝𝑝𝑜𝑜 , 𝑐𝑐 ( 𝑡𝑡 𝑘𝑘 ) ∣ − 0.6 ∙ ∣ ∆𝑅𝑅 𝑝𝑝𝑜𝑜𝑙𝑙𝑙𝑙 , 𝑐𝑐 ( 𝑡𝑡 𝑘𝑘 ) ∣ .

Short rate shock : Assume the bank uses time bands and t K = 25 years (the midpoint (in time) of the longest tenor bucket ), where is the midpoint (in time) for bucket k. For with t k 𝐾𝐾 = 19 = 3.5 years, the scalar adjustment 𝐾𝐾 for the 𝑡𝑡 𝑘𝑘 short shock would be: −3 .⁵ = 𝑘𝑘 0.417. = 10 Banks would multiply this by the value of the short rate shock to obtain the amount⁴ to be added or subtracted from the yield curve at that tenor point. If the short 𝑆𝑆 𝑠𝑠ℎ𝑜𝑜𝑝𝑝𝑜𝑜 rate ( 𝑡𝑡 shock 𝑘𝑘 )= 𝑒𝑒 was +250 bps, the

increase in the yield curve at t k = 3.5 years would be 104.2 bps.

Steepener: Assume the same point on the yield curve as above, t k = 3.5 years. If the absolute value of the short rate shock was 250 bps and the absolute value of the long rate shock was 100 bps (as for the euro), the change in the yield curve at t k = 3.5 years would be the sum of the effect of the short rate shock plus the effect of the long rate shock in basis points: . − 0.65 ∙ 250 bps ∙ 0.417+ 0.9 ∙ 100 bps ∙ (1 − 0.417)= − 15.3 bps Flattener: The corresponding change in the yield curve for the shocks in the example above at t k = 3.5 years would be: .

+ 0.8 ∙ 250 bps ∙ 0.417 − 0.6 ∙ 100 bps ∙ (1 − 0.417)= 48.4 bps

²⁰ The value of in the denominator of the function −𝑡𝑡 k controls the rate of decay of the shock. 𝑥𝑥 𝑥𝑥 𝑒𝑒 51