## 1dnkea2020007

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### EXECUTIVE SUMMARY — overview
- COVID-19 pandemic: FSAP work conducted prior to the COVID-19 pandemic; this Technical Note (TN) does not assess the impact of the crisis or recent crisis-related policy measures. Findings and recommendations remain pertinent given focus on financial system structure and vulnerabilities.
- Size of the financial system: Denmark’s financial system size described as "large" at 630 percent of GDP.
- New data infrastructure and multi-layer contagion model:
  - Novel multi-layer contagion model built on a new database reconciling securities data and the newly-released confidential credit register.
  - Model distinguishes eight exposure types (layers): loans, deposits, reverse repos, covered bonds, other debt securities, equities, unlisted shares, and other claims.
  - Simulation exercise: series of idiosyncratic shocks with iterative default triggering.
  - Repricing channel on traded securities introduced to capture cascade effects from market reactions to changes in entities’ solvency.
- Scope: Focus on banking system (banks and MCIs), interconnections via covered bond market, exposures vis-à-vis insurers, pension and investment funds, households and corporates, domestically and abroad.

### ROLE OF MCIs AND COVERED BONDS
- Centrality of MCIs:
  - MCIs play a central role in the domestic interbank system and interconnect systemic and non-systemic banks through covered bond exposures.
- Covered bonds and interconnectedness:
  - Covered bonds widely held by banks and institutional investors, receive exemptions from large exposure limits, qualify as HQLA, and typically have very high ratings.
  - Small number of covered bond issuers increases likelihood that problems in one MCI could spread system-wide.

### HOUSEHOLD WEALTH COMPOSITION AND VULNERABILITIES
- Composition (shares of household wealth):
  - Housing wealth: 37 percent.
  - Pension and life-insurance entitlements: 33 percent.
  - Investment fund shares: 5 percent.
  - Deposits at banks: 15 percent of household financial assets.
- Key vulnerabilities and channels:
  - Danish household indebtedness among highest in advanced economies.
  - Financing conditions from MCIs and banks critical for households; shocks to covered bond risk premium or MCI solvency/liquidity could raise household refinancing costs.
  - Housing downturn scenario: direct shock to housing wealth (37 percent) plus indirect losses through pension wealth (33 percent).
  - Confluence of adverse interest rate, asset price, and income shocks could reinforce macrofinancial feedback loops increasing household consumption vulnerability.

### DATA, NETWORK CONSTRUCTION, AND INSTRUMENT BREAKDOWN
- Core network composition:
  - 21 largest Danish credit institutions: 5 SIFI banks; 9 non-SIFI (Tier 2) banks; 7 MCIs.
  - Core network share of total assets of Danish banking sector: 86 percent.
  - Full network size when extended: 1,005 nodes (entities + sector aggregates).
- Selected network and balance-sheet magnitudes (system map, December 2018):
  - Total (network map heatmap) = 39,301 (billions DKK).
  - Credit institutions intragroup exposures: 24 percent of overall exposures.
  - Rest of the world (ROW) funding source for credit institutions: 32 percent of liabilities.
  - Household deposits: 13 percent of funding sources of credit institutions.
  - Insurance sector assets with banks and MCIs: 25 percent.
  - Debt securities in insurers' exposures to banks and MCIs: 88 percent.
  - Pension funds' exposure to government securities: 17 percent.
  - Pension funds' exposures to credit institutions: debt securities 72 percent; deposits 16 percent.
- Exposures categorized into 8 instrument types (sources noted in TN) and shares of total exposures:
  - Loans: 27%
  - Equity: 25%
  - Covered bonds: 20%
  - Other bond: 18%
  - Repos: 5%
  - Other: 3%
  - Deposits: 1%
  - Unlisted Shares: 1%
- Notes on covered bond exposures:
  - Direct exposures to covered bonds account for 20 percent; indirect exposures underlying loans equal 59 percent (would raise effective covered bond exposure if included).
- Data limitations:
  - Deposits from non-reporting credit institutions and loans from non-reporting credit institutions to Danish counterparties not included.
  - Holdings of Danish securities by foreign entities lack investor sector and country detail; grouped as "RoW".

### NETWORK TOPOLOGY AND ROLE OF MCIs
- Visualization and thresholds:
  - Core network interbank topology depicts MCIs centrally; exposures below thresholds excluded (<10 percent of exposed entity’s capital in one panel; <5 percent in another).
- Structural features:
  - MCIs link systemic and non-systemic banks through dense covered bond exposures.
  - Strong connections between Danish banking system and domestic corporate sector (notably CRE), households (loans), and domestic institutional investors (securities).
  - Cross-border exposures concentrated with Nordic region and the euro area.

### MULTI-LAYER CONTAGION MODEL — FRAMEWORK HIGHLIGHTS
- Model provenance and extensions:
  - Based on CoMap (Covi, Gorpe and Kok, 2019) with credit and funding channels retained and a market repricing loop added.
  - Repricing loop treats covered bonds with specific uplift buffer mechanics.
- Credit channel formula (as presented):
  - LOSS_i^Credit = sum_{j in Y} sum_k eta_{ij}^k * lambda_{ij}^k * x_{ij}^k
- Funding channel and deleveraging mechanics (as presented):
  - TFS_i = sum_{j in Y} sum_k rho_{ji}^k * x_{ji}^k
  - remaining_shortfall = max{0, sum_{j in Y} sum_k rho_{ji}^k * x_{ji}^k - gamma_i}
  - LOSS_i^Funding = delta_i * min{ (1/(1-delta_i)) * max{0, sum_{j in Y} sum_k rho_{ji}^k * x_{ji}^k - gamma_i}, theta_i }
- Market repricing loop steps (as presented):
  1. Map capital ratio c_{j,t} and macro profile M_t to rating category R_{j,t} = g(c_{j,t}, M_t).
  2. Rating migration determines change in yield spread Δy_{j}^k = f(R_{j,t}, R_{j,t-1}, k); covered bonds incorporate uplift buffer.
  3. Price impact ΔP_{ij}^k = mu_{ij}^k * Δy_{j}^k, where mu_{ij}^k is modified duration.
  4. Valuation losses LOSS_i^{Repricing} = sum_{j in Y} sum_k P_{ij}^k * x_{ij}^k; loop iterates until no further downgrades.
- Other features:
  - Reverse repos mapped to underlying securities; lender takes ownership at latest market prices on counterparty default.
  - Group intra-group recapitalization allowed: parent may inject capital to bring child above buffer if parent can afford it.
- Default conditions:
  - Insolvency default when c_{i,t} - c_{i,min} < LOSS_i^{Credit} + LOSS_i^{Funding} + LOSS_i^{Repricing}.
  - Illiquidity default when theta_i < (1/(1-delta_i)) * max{0, sum rho_i x_{ji} - gamma_i}.
- Simulation algorithm: sequential default algorithm with steps i–vii (reverse repos settled; obligations defaulted; funding withdrawals and deleveraging; market repricing loop; potential intra-group recapitalization; reevaluation; iterate until no new defaults).

### MODEL CALIBRATION — key parameter specifications
- Granularity: parameters calibrated at highest granularity possible using bank-specific and exposure-specific data.
- Loss-given-default (LGD):
  - Loans, deposits, reverse repos and other claims: LGD = allocated value of protection reported by credit institution to credit register (in percent of exposure).
  - Covered bonds and other debt securities: LGD updated dynamically in repricing module based on distance-to-default.
  - Equity and unlisted shares: LGD assumed to be 100 percent.
- Modified duration:
  - Used for covered bonds and other debt securities; equals average weighted by size of exposures.
  - Defined: Modified Duration = Macaulay Duration / (1 + YTM / n).
  - For Danish callable covered bonds, option adjusted modified duration used.
- Funding shortfall calibration:
  - Calibrated at exposure level by difference between reference date (September 30, 2019) and maturity date.
  - Maturity buckets with two thresholds: within next month; within next three months. First threshold consistent with LCR (30-day scenario); second used for sensitivity testing.
- Default threshold:
  - Based on CET1 definition of regulatory capital, with minimum ratio plus pillar 2 adjustments setting threshold. Sensitivity analysis uses higher threshold including capital conservation, countercyclical and SIFI buffers.
- Liquidity surplus (gamma_i): stock of HQLA in excess of NLO over 30-day scenario; HQLA and NLO reported on LCR templates (C.72.00-C.76.00).
- Liquidity constraint (theta_i): total amount of unencumbered non-central bank eligible assets from Asset Encumbrance templates (F.32.01).
- Discount rate (delta_i): estimated per bank based on portfolio of unencumbered assets weighted by haircuts; haircuts based on ECB guidelines with lower bound applied.
- Capital-to-rating conversion:
  - Rating mapped solely as a function of issuer’s capital and macro profile M_t on scale very weak minus (14) to very strong plus (0); baseline macro profile assumed "moderate".
- Rating migration matrix:
  - Changes in bond yield spreads calibrated using Hull et al. (2005) historical results; mapping accounts for covered bond uplift buffer and expressed in basis points.

### SIMULATION OUTPUTS AND INDICES
- Simulation outputs:
  - Number of defaults caused by each trigger event.
  - Losses incurred by each entity in network per simulation.
- Indices constructed for core network:
  - Contagion index (CIcore_i) = 100 * ∑_{j∈C} (L_{j,i} / c_j).
  - Vulnerability index (VIcore_i) = 100 * (∑_{j∈C} L_{i,j}) / (N_core * c_i).
  - Overall vulnerability index for full network (VI_i) = 100 * (∑_{j∈F} L_{i,j}) / (N_F * c_i).

### KEY SIMULATION FINDINGS — contagion, channels, vulnerabilities
- Primary sources and transmission:
  - Danish banks and MCIs mostly exposed to shocks originating within the banking system.
  - MCIs are key sources of outward spillovers and induce highest contagion losses through unlisted shares (reflecting complex group structures) and covered bond exposures.
  - Contagion transmitted predominantly through credit losses.
  - Repricing channel cascade effects materially affect only one non-systemic bank in the simulations.
- Systemic vs non-systemic institutions:
  - Systemic banks, on average, more vulnerable to inward spillover losses due to covered bond holdings.
  - Domestic banking system susceptible to cross-border spillovers from Nordic region and the euro area (via interbank loans and deposits).
  - Cascade effects from losses in subsequent rounds within the banking system remain limited.
  - Four credit institutions identified with ability to amplify spillovers (individual financial institutions, not consolidated groups).
- Top contagion contributors and magnitudes:
  - Half of top-20 most contagious nodes are Danish credit institutions: among them five MCIs, three systemic banks, two non-systemic banks.
  - MCIs induce highest contagion losses collectively and individually; two MCIs rank in top three.
  - Unlisted shares account for majority of MCI contagion losses, followed by covered bonds.
- Cross-country spillovers:
  - Banking sectors at country level from Nordic region and euro area may generate significant spillovers.
  - Highest contagion index in exercise: 12.3 percent, generated mainly through interbank loans and deposits when default of entire banking system of a euro area member state used as trigger.
- Vulnerability indices and attributions:
  - Highest VIcore associated with an MCI incurring average losses of about 4.5 percent of its capital from failures in core network.
  - Covered bonds contribute largest share to core network’s vulnerabilities, followed closely by unlisted shares.
  - Deposit-related losses for MCIs partly due to temporary spike in deposits observed on September 30, 2019.
  - When full network considered, systemic banks’ average overall vulnerability index is three times higher than that of MCIs.
  - Overall vulnerability indices lower (about one to ten times) than core vulnerability indices due to dilution from increasing network size from 21 to 1005 nodes.
- Cascade effects and risk map:
  - Repricing channel and knock-on effects limited in amplification; covered bonds’ short durations and high initial ratings with uplift buffers restrain valuation losses from credit spreads.
  - Low number of contagion defaults observed; defaults associated with smaller non-systemic banks or intra-group entities.
  - Risk Map identifies four entities relatively high on both contagion and vulnerability indices (dark-shaded quadrant).

### SENSITIVITY TESTS AND ROBUSTNESS
- Rating conversion and migration:
  - Baseline macro = "moderate"; alternative "weak" and "strong" macro profiles tested.
  - Little sensitivity: alternative assumptions do not materially change contagion and vulnerability indices or entity rankings.
  - Explanation: small share of contagion losses associated with market pricing mechanism.
- Funding shortfall ratio:
  - Raising short-term threshold from one month to three months yields no additional contagion losses.
  - Explanation: banks’ liquidity buffers can withstand increased withdrawals; observed average increase in liquidity received through central bank credit facility (DN Credit Facility) in percent of NLO.
- Default ratio for households and NFCs:
  - Default ratio increased in 5 percentage point increments up to 100 percentage points to detect tipping points.
  - Household and Real Estate contagion losses almost entirely linear with respect to default rate; no tipping points detected.
- Default threshold:
  - Raising default threshold to include regulatory buffers (capital conservation buffer 2.5 pct; SIFI buffer 0-3 pct; countercyclical capital buffer 1-1.2 pct) increases overall contagion losses.
  - Ranking of entities changes noticeably; some entities’ contagion indices almost triple when buffers included.
- Overall robustness:
  - Findings broadly robust to alternative assumptions and calibrations; main exception is sensitivity to default threshold including buffers.

### CAVEATS, DATA LIMITATIONS, AND MODEL BOUNDARIES
- Repricing channel limited to credit-spread-driven valuation changes; market liquidity shocks (selling pressures) not incorporated due to data limitations — inclusion would likely increase overall contagion and role of repricing channel.
- Single datapoint: September 30, 2019 — on that date MCIs had very high liquidity from large mortgage refinancing flows (temporary), potentially overstating deposit-related losses.
- Aggregation and sector treatment:
  - Danish OFIs, investment funds, governmental entities and cross-border exposures aggregated as sector nodes; trigger shock implies default of entire sector for those nodes.
- Solo-level analysis:
  - Entities considered at solo level; largest SIFIs are groups. Group structures imply intra-group unlisted share ownership drives large losses when subsidiaries default (~90 percent of unlisted shares in core represent intra-group; ~75 percent in full network).
- Data gaps:
  - Significant gaps remain (non-bank wholesale funding, foreign ownership of securities, non-bank and foreign financial entity balance sheets); partial coverage of outward spillovers may underestimate contagion risks and feedback loops with Nordic and euro area sectors.

### CONCLUSIONS AND POLICY IMPLICATIONS
- Main conclusions:
  - Contagion risk strongest within banking system due to intra-group exposures and cross-ownership of covered bonds.
  - MCIs are key potential contagion sources.
  - Systemic banks have higher vulnerability indices than MCIs and non-systemic banks; vulnerabilities stem from within banking system and other sectors.
  - Credit channel is primary propagation channel for contagion losses.
  - Nordic region and euro area banking systems are significant sources of cross-border spillovers to Denmark.
- Key recommendations (from Table 1; authority and timeframe as in source):
  - Close data gaps, including coverage and quality of bilateral exposures (asset and liability positions) of financial entities, and enhance data infrastructure to link securities data and credit register with balance sheets of financial entities. Authority responsible: Danmarks Nationalbank (DN). Timeframe: ST (Short term, 1-3 years).
  - Develop a system-wide contagion risk model and incorporate contagion effects into overall macroprudential stress testing framework for regular systemic risk monitoring. Authority responsible: DN. Timeframe: ST (Short term, 1-3 years).
  - Map all interlinkages of the covered bond market and model transmission through different financial intermediaries and the real sector.
  - Strengthen macroprudential stress-testing framework by incorporating contagion effects across financial institutions.

*Source: EXECUTIVE SUMMARY and excerpts from Denmark Technical Note (CoMap contagion analysis), IMF/Danmarks Nationalbank; supervisory data; IMF staff calculations; reference date September 30, 2019.*

### EXECUTIVE SUMMARY __________________________________________________________________________ 5

### EXECUTIVE SUMMARY

### Introduction
- COVID-19 pandemic: The FSAP work was conducted prior to the COVID-19 pandemic, so this Technical Note (TN) does not assess the impact of the crisis or the recent crisis-related policy measures. Nonetheless, given the FSAP’s focus on financial system structure and vulnerabilities, the findings and recommendations of the TN remain pertinent.
- Size of the financial system: Denmark’s financial system is described as "large" at 630 percent of GDP.

### New data infrastructure and multi-layer contagion model
- Data and model:
  - A novel multi-layer contagion model was developed based on a new and comprehensive database reconciling securities data and the newly-released confidential credit register.
  - The model distinguishes transmission of shocks between eight different exposure types or layers: loans, deposits, reverse repos, covered bonds, other debt securities, equities, unlisted shares, and other claims.
  - The simulation exercise consists of a series of idiosyncratic shocks where the default of each node is triggered iteratively.
  - The model introduces a repricing channel on traded securities to capture cascade effects arising from market reactions to changes in an entity’s solvency condition.
- Scope:
  - The exercise focuses on the banking system (banks and MCIs), and on interconnections through the covered bond market, while also including exposures vis-à-vis non-bank financial institutions (insurer, pension and investment funds) and non-financial sectors (households, corporates), both domestically and abroad.
  - The network analysis builds on the CoMap (Covi, Gorpe, and Kok 2019) framework to develop the multi-layer model with eight instrument types and a market repricing channel.

### Role of MCIs and covered bonds
- Centrality of MCIs:
  - MCIs play a central role in the domestic interbank system and take center stage in the network, interconnecting systemic and non-systemic banks through covered bond exposures.
  - Covered bonds are a mainstay of the Danish mortgage system and have a large presence in domestic and foreign portfolios.
- Covered bonds and interconnectedness:
  - Covered bonds contribute to increased interconnectedness because they are widely held by banks and institutional investors, receive exemptions from large exposure limits, qualify as HQLA, and typically have very high ratings.
  - The small number of covered bond issuers increases the likelihood that problems in one MCI could spread system-wide.

### Key findings on contagion, channels, and vulnerabilities
- Primary sources and transmission:
  - The analysis reveals that Danish banks and MCIs are mostly exposed to shocks originating within the banking system.
  - MCIs are a key source of outward spillovers and induce the highest levels of contagion losses through unlisted shares (reflecting complex group structures) and covered bond exposures.
  - Contagion is transmitted predominantly through credit losses.
  - Cascade effects owing to the repricing channel (which captures market reactions to weakening capitalization of MCIs and banks) affect materially only one non-systemic bank in the simulations.
- Systemic vs non-systemic institutions:
  - Systemic banks, on average, are more vulnerable to inward spillover losses owing to their covered bond holdings.
  - The domestic banking system is susceptible to cross-border financial spillovers from the Nordic region and the euro area (including via interbank loans and deposits).
  - Cascade effects from losses in subsequent rounds within the banking system remain limited.
  - The analysis identifies four credit institutions with the ability to amplify spillovers across the financial system (these are individual financial institutions, not consolidated groups).
- Network and balance-sheet magnitudes (selected figures from system map, December 2018):
  - Total (network map heatmap) = 39,301 (billions DKK).
  - Credit institutions intragroup exposures account for 24 percent of overall exposures.
  - Rest of the world (ROW) is a key funding source for credit institutions at 32 percent of liabilities.
  - Household deposits account for 13 percent of the funding sources of credit institutions.
  - The insurance sector holds a significant share of assets with banks and MCIs equal to 25 percent.
  - Debt securities make up 88 percent of insurers' exposures to banks and MCIs.
  - Pension funds' exposure to government securities is 17 percent.
  - Pension funds' exposures to credit institutions are predominantly in debt securities and deposits with 72 and 16 percent shares, respectively.

### Interconnectedness: cross-sectoral and cross-border linkages
- Cross-sectoral connections:
  - Credit institutions are at the core and are highly interconnected through loans, guarantees, fixed income (including covered bonds), and ownership links within financial group structures.
  - Pension funds and insurance companies have significant exposures to credit institutions and could amplify stress mainly through liquidation of large covered bond holdings (fire sales).
  - Households hold pension and housing wealth constituting around 70 percent of their wealth (see Figure 3 reference in source).
  - Non-financial corporate (NFC) intra-linkages are notable: exposures among NFCs are highlighted as being composed of 75 percent equity/shares and 25 percent intercompany lending—the highest of any intersectoral linkages in the system.
- Cross-border linkages:
  - Cross-border exposures are significant for all sectors and are concentrated vis-à-vis the Nordic region and the euro area.

### Institutional investors
- Insurance companies:
  - Hold sizable assets with banks and MCIs (25 percent).
  - Their exposures to credit institutions are mostly in debt securities (88 percent).
  - Foreign assets make up about one-third of insurers' balance sheets and are dominated by equity investments.
  - On the liabilities side, households are the prime market for insurers; insurers also have short-term liabilities vis-à-vis banks.
- Pension funds:
  - Have a diversified domestic portfolio with significant exposure to government securities (17 percent).
  - Exposures to credit institutions are predominantly in debt securities and deposits with 72 and 16 percent shares, respectively.
  - Place about one-fifth of their portfolio with investment funds.
  - On the liabilities side, apart from technical provisions due to households, pension funds have short-term debt liabilities vis-à-vis both domestic and foreign banks.
- Investment funds:
  - Portfolio almost equally split between fixed income and equity securities.
  - Half of fixed income portfolio comprises debt securities of domestic credit institutions, corresponding to around one quarter of their assets.
  - Of the equity portfolio, 75 percent is invested abroad while the rest is mostly held as shares in other funds.

### Key recommendations (Table 1)
- Close data gaps, including the coverage and quality of bilateral exposures (asset and liability positions) of financial entities, and enhance the data infrastructure to link securities data and credit register with balance sheet of financial entities. Authority responsible: Danmarks Nationalbank (DN). Timeframe: ST (Short term, 1-3 years).
- Develop a system-wide contagion risk model and incorporate these contagion effects into the overall macroprudential stress testing framework, which can then also be used for regular systemic risk monitoring. Authority responsible: DN. Timeframe: ST (Short term, 1-3 years).

*Source: EXECUTIVE SUMMARY, Denmark Technical Note (CoMap contagion analysis), IMF/Danmarks Nationalbank.*

### 9.      Housing and pension wealth make up the vast majority of household wealth (Figure

### 9. Housing and pension wealth make up the vast majority of household wealth (Figure 3)

### Household wealth composition and vulnerabilities
- Housing wealth: 37 percent share of total household wealth.
- Pension and life-insurance entitlements: 33 percent share of household wealth.
- Investment fund shares: 5 percent share of household wealth.
- Deposits at banks: 15 percent of household financial assets (largest deposit base for banks).
- Key vulnerabilities and channels:
  - Danish household indebtedness is among the highest in advanced economies.
  - Financing conditions offered by MCIs and banks are of critical importance to households.
  - Significant adverse shocks that impact the risk premium of covered bonds or undermine solvency or liquidity conditions for MCIs could translate into higher refinancing costs for households.
  - A weakening balance sheet position of institutional investors could further exacerbate household distress through reductions in pension wealth.
  - In a housing market downturn scenario, households could face a double whammy: (i) a direct shock to housing wealth (37 percent share) and (ii) indirect losses through asset prices impacting pension wealth (33 percent share).
  - A confluence of adverse interest rate, asset price, and income shocks could reinforce macrofinancial feedback loops, increasing household consumption vulnerability.

*Sources: Danmarks Nationalbank, DN Financial Stability Report, IMF staff calculations.*

### Coverage and exposure data — network construction and composition
- Core network: 21 largest Danish credit institutions comprising:
  - 5 SIFI banks
  - 9 non-SIFI (Tier 2) banks
  - 7 MCIs
- Core network share of total assets of the Danish banking sector: 86 percent.
- Full network size when extended to non-bank financial entities and other sectors/countries: 1,005 nodes (combining individual entities and sector-level aggregates).
- Table 2 (network composition by type and location) summary (as presented in source):
  - Core: 305 (Denmark) and 700 (Rest of the World) totals shown in table as "Full All  305 700".
  - Sector/Entity counts in core and non-core include: Credit institutions, Pension funds, Insurance companies, Investment funds (sector aggregate), Other financial entities (sector aggregate), Households (sector aggregate), NFCs (industry aggregates), Government, RoW.
- Shares and exposures:
  - Core network has the largest share of exposures within the network at 42 percent.
  - Core network accounts for 29 percent of the total obligations.
  - Rest of the world (RoW) has 7 percent of exposures to the Danish financial system versus 26 percent of liabilities towards Danish entities.

### Exposure data and instrument breakdown
- Primary micro-data sources: securities statistics and the new credit register, enriched with counterparty information from the business register and other sources.
- Exposures categorized into 8 instrument types (Table 3):
  - Loans (credit register, carrying amount)
  - Deposits (interbank) (credit register, carrying amount) — available if depositor is a reporting credit institution
  - Reverse repos (credit register, carrying amount) — including information on underlying security; included when one involved counterparty is a reporting credit institution
  - Other loans (credit register, carrying amount)
  - Covered bonds (securities statistics, market value)
  - Other debt securities (securities statistics, market value)
  - Equity (securities statistics, market value)
  - Unlisted equity/shares (several sources, book value)
- Shares by instrument type (share of total exposures):
  - Loans: 27%
  - Equity: 25%
  - Covered bonds: 20%
  - Other bond: 18%
  - Repos: 5%
  - Other: 3%
  - Deposits: 1%
  - Unlisted Shares: 1%
- Notes on covered bond exposures:
  - Direct exposures to covered bonds account for 20 percent.
  - This ratio would be significantly higher if indirect exposures (those underlying loans: 59 percent) and repos are considered.
- Data limitations:
  - Data do not include deposits from non-reporting credit institutions and loans provided to Danish counterparties from non-reporting credit institutions.
  - For holdings of Danish securities by foreign entities, investor sector and country information is not available; these are grouped as "RoW".

### Network topology and role of MCIs
- Visualization approach:
  - Core network interbank topology: red nodes (MCIs) positioned centrally and connected to systemic (blue) and non-systemic (green) banks. Line thickness proportional to exposure-to-capital ratio; node size proportional to number of exposures weighted by exposure-to-capital ratio.
  - Full network: two concentric circles — inner circle is the core network; outer circle includes most important counterparts with material exposures to the core.
  - Exposures below thresholds are excluded: less than 10 percent of exposed entity’s capital in top panel; less than 5 percent in bottom panel.
- Key structural features:
  - MCIs play a central role, linking systemic and non-systemic banks through a dense network of covered bond exposures.
  - Strong connections exist between the Danish banking system and domestic corporate sector (in particular, CRE) and household sectors (via loans), and domestic institutional investors (insurers, pension and investment funds) via securities.
  - Cross-border exposures are especially strong with the Nordic region and the euro area financial system.

### Contagion modeling framework (Multi-layer Contagion Mapping Model — CoMap extensions)
- Modeling framework:
  - Started from CoMap (Covi, Gorpe and Kok, 2019) and maintained credit and funding transmission channels.
  - Key extensions include a market repricing loop to capture market reactions to changes in entities’ capitalization ratios — important for covered bonds, which are treated differently due to potential uplift buffer.
- Credit channel (losses from defaults):
  - Loss to bank i via credit channel:
    LOSS_i^Credit = sum_{j in Y} sum_k eta_{ij}^k * lambda_{ij}^k * x_{ij}^k
    - where eta_{ij}^k is default ratio, lambda_{ij}^k is exposure-specific loss-given-default, x_{ij}^k is claim of type k on bank j.
- Funding channel (funding shortfalls from withdrawals):
  - Total funding shortfall to bank i:
    TFS_i = sum_{j in Y} sum_k rho_{ji}^k * x_{ji}^k
    - where rho_{ji}^k is funding shortfall rate specific to each exposure.
  - Bank i can pledge surplus HQLA (excess of net liquidity outflows–NLO), gamma_i, to central bank to offset TFS:
    remaining_shortfall = max{0, sum_{j in Y} sum_k rho_{ji}^k * x_{ji}^k - gamma_i}
  - If remaining_shortfall > 0, bank i may deleverage by selling unencumbered marketable assets (limited pool theta_i) at a discount delta_i:
    LOSS_i^Funding = delta_i * min{ (1/(1-delta_i)) * max{0, sum_{j in Y} sum_k rho_{ji}^k * x_{ji}^k - gamma_i}, theta_i }
- Market repricing channel (endogenous price and rating effects):
  - Steps in market repricing loop:
    1. Map capital ratio c_{j,t} and macro profile M_t to a rating category: R_{j,t} = g(c_{j,t}, M_t).
    2. Rating migration (from R_{j,t-1} to R_{j,t}) determines change in yield spread for security k: Δy_{j}^k = f(R_{j,t}, R_{j,t-1}, k). Covered bonds incorporate an uplift buffer before downgrade.
    3. Price impact on holder i for exposure to j,k: ΔP_{ij}^k = mu_{ij}^k * Δy_{j}^k, where mu_{ij}^k is modified duration.
    4. Valuation losses L O S S_i^{Repricing} = sum_{j in Y} sum_k P_{ij}^k * x_{ij}^k; resulting valuation losses can cause further downgrades and iterate until no further price impacts/downgrades occur.
  - Market price impact takes into account:
    - issuer (capital ratio), type of security (covered bonds treated differently), and maturity as captured by modified duration.
- Other model features:
  - Reverse repos and underlying securities are fully accounted for: reverse repo exposures are mapped to underlying securities, with maturity, modified duration and LGD characteristics; if a reverse repo counterparty defaults the lender takes ownership of underlying securities at latest market prices and may incur losses from prior repricing.
  - Group structure and intra-group recapitalization: when an entity’s capital falls below default threshold it may receive capital injection from an able parent sufficient to bring capital above a buffer, reducing parent capital by same amount; if parent cannot recapitalize daughter, daughter defaults.
- Default conditions:
  - Insolvency default: after credit, funding and market repricing losses and intra-group recapitalization, bank defaults due to insolvency if:
    c_{i,t} - c_{i,min} < LOSS_i^{Credit} + LOSS_i^{Funding} + LOSS_i^{Repricing}
  - Illiquidity default: bank is illiquid if it has used all HQLA buffer and pool of unencumbered marketable securities:
    theta_i < (1/(1-delta_i)) * max{0, sum rho_i x_{ji} - gamma_i}
- Algorithm and simulation sequence (sequential default algorithm):
  - At the outset, an idiosyncratic shock (default of an entity) triggers sequence:
    i. Reverse repos associated with the defaulted entity are settled and underlying securities transferred to lender;
    ii. The entity defaults on obligations resulting in losses to counterparts based on up-to-date LGDs;
    iii. The entity withdraws funding leading to funding shortfalls in affected counterparts;
    iv. Counterparts deleverage if they cannot meet funding shortfalls using liquidity buffers;
    v. Market repricing loop kicks in if preceding losses lead to rating downgrades; iterates until no further downgrades;
    vi. Potentially insolvent banks receive recapitalization, if available, from solvent parents;
    vii. Solvency and liquidity positions are reevaluated to determine additional defaults.
  - If new defaults occur, steps i–vii are repeated until no new defaults in a round.

*Source: https://www.imf.org/-/media/files/publications/cr/2020/english/1dnkea2020007.pdf*

### 30.      It is important to note that while all nodes in the network are allowed to trigger an

### 1dnkea2020007 - 30.      It is important to note that while all nodes in the network are allowed to trigger an 

### Calibrating Model Parameters
- Model parameters are calibrated at the highest level of granularity possible based on bank-specific and, to the extent possible, exposure-specific data (paragraph 31).
- Loss-given-default (흀풊풋풌)
  - For loans, deposits, reverse repos and other claims: LGD is the allocated value of the protection to the exposure as reported by the credit institution to the credit register in per cent of the exposure amount. The allocated value of the protection is defined as the maximum amount of the protection value that can be considered as credit protection for the instrument following the collateral allocation principles used by the credit institution for internal risk management purposes. There is no requirement that the scope of protection items is aligned with the protection items eligible for credit risk mitigation in accordance with the CRR (paragraph 32).
  - For covered bonds and other debt securities: LGD is updated dynamically in the repricing module based on the distance-to-default from the current state (paragraph 32).
  - For equity and unlisted shares: LGD is assumed to be 100 percent (paragraph 32).
- Modified Duration (흁풊풋풌)
  - Defined for covered bonds and other debt securities and used in the repricing module. Data equals the average weighted by the size of the exposures (paragraph 33).
  - Defined as: Modified Duration = Macaulay Duration / (1 + YTM / n), where: YTM = Yield To Maturity and n = number of coupon periods per year (paragraph 33).
  - For Danish callable covered bonds, the option adjusted modified duration is used due to negative convexity when the bond's price exceeds 100 (paragraph 34).
- Funding Shortfall (흆풊풋풌)
  - Portion of withdrawn funding assumed not to be rolled over when the funding provider defaults or gets into distress (paragraph 35).
  - Calibrated at exposure level by difference between reference date (September 30, 2019) and maturity date. Exposures divided into maturity buckets with two thresholds for short-term liabilities:
    - Exposures with maturity within the next month.
    - Exposures with maturity within the next three months (paragraphs 35–36).
  - First threshold consistent with the Liquidity Coverage Ratio, LCR, which assumes a 30-day liquidity distress scenario; second threshold used for sensitivity testing over a longer period (paragraph 36).
- Default Threshold (풄풊,풎풊풏)
  - Based on CET1 definition of regulatory capital, with minimum ratio plus the pillar 2 adjustments setting the threshold. Sensitivity analysis uses a higher threshold that includes the additional capital conservation, counter cyclical and SIFI buffers (paragraph 37).
- Liquidity Surplus (휸풊)
  - Calculated as the stock of HQLA in excess of net liquidity outflows (NLO) over a 30-day liquidity distress scenario. Both HQLA and NLO reported on Liquidity Coverage Ratio templates (C.72.00-C.76.00) (paragraph 38).
- Liquidity Constraint (휽풊)
  - Calibrated as the total amount of unencumbered non-central bank eligible assets reported in Asset Encumbrance templates (F.32.01) (paragraph 39).
- Discount Rate (휹풊)
  - Used in fire sale; estimated per bank based on portfolio of unencumbered non-central bank eligible assets weighted by relevant haircuts. Haircut rates based on ECB guidelines after applying a lower bound haircut, the highest haircut used for the respective central bank eligible instruments (paragraph 40).
- Capital-to-rating Conversion (품)
  - Rating is solely a function of issuer’s capital; changes in yield spreads due to rating downgrades are purely a credit spread (paragraph 41).
  - Capital ratio is mapped to a rating category based on methodology used by credit rating agencies. Dynamic assignment of rating categories is a function of a bank’s capital adequacy, 푐푗,푡, and the general macro profile of the country, 푀푡, at time 푡. Macro profile mapped on scale: very weak minus (14) to very strong plus (0), with moderate (7) in the middle. For the main exercise, macro profile assumed to be moderate; sensitivity tested to more and less strict conditions (paragraph 41).
- Rating Migration Matrix (풇)
  - Changes in bond yield spreads calibrated using Hull et al. (2005) historical results. After interpolating yield spreads for full tier of rating categories, a migration matrix maps changes in rating categories to changes in yield spreads; mapping accounts for uplift buffer of covered bonds by issuer. Resulting changes expressed in basis points (paragraph 42).

### Results — Simulation Outputs and Indices
- Simulation exercise: series of idiosyncratic shocks where default of each entity is triggered iteratively to produce:
  - Number of defaults caused by the trigger event.
  - Losses incurred by each entity in the network in each simulation (paragraph 43).
- Indices constructed for the core network:
  - Contagion index (CIcore):
    - CIcore_i = 100 * ∑_{j∈C} (L_{j,i} / c_j), where L_{j,i} is j′s losses induced by i and c_j is j′s capital (paragraph 43).
    - CIcore captures contagion to the core network induced in each simulation triggered by node i, taking weighted average of all core banks' losses in percent of their capital (paragraph 43).
  - Vulnerability index (VIcore):
    - VIcore_i = 100 * (∑_{j∈C} L_{i,j}) / (N_core * c_i), where N_core is number of core entities; L_{i,j} and c_i as before (paragraph 43).
    - VIcore is average loss experienced by entity i over simulations induced by other core entities (paragraph 43).
  - Overall VI (full network):
    - VI_i = 100 * (∑_{j∈F} L_{i,j}) / (N_F * c_i), where N_F is number all entities (paragraph 43).

### Appraisal of Contagion Risks (Key findings)
- Danish credit institutions are mostly exposed to shocks from within the banking system (paragraph 46).
- Top-20 contagion contributors:
  - Half of the top 20 most contagious nodes are Danish credit institutions; among them five are MCIs, three are systemic banks, two are non-systemic banks (paragraph 46).
- MCIs:
  - MCIs induce the highest levels of contagion losses collectively and individually; two MCIs rank in the top three (paragraph 46).
  - Unlisted shares account for majority of MCI contagion losses (reflecting complex group structures), followed by covered bond exposures (paragraph 46).
- Systemic banks:
  - Generate far less contagion losses but transmit shocks through a more diverse set of instruments, with covered bonds having the largest contribution (paragraph 46).
- Cross-country spillovers:
  - Banking sectors at country level from Nordic region and euro area may generate significant spillovers. Highest contagion index in the exercise is 12.3 percent, generated mainly through interbank loans and deposits when default of the entire banking system of a euro area member state is used as the trigger event (paragraph 46).
- Transmission channels:
  - Contagion transmitted predominantly through credit losses.
  - Repricing channel cascade effects visible under two simulations (default of one MCI and one non-systemic bank), mainly affecting one other non-systemic bank (paragraph 46).
  - Funding channel losses are very limited due to banks’ liquidity buffers in most cases (paragraph 46).

### Identifying Vulnerabilities in the System
- Vulnerability decomposition and rankings (paragraph 47):
  - Systemic banks are more vulnerable to shocks from within the banking system, although average VI of MCIs and non-systemic banks do not differ significantly (paragraph 47).
  - Highest vulnerability index associated with an MCI which incurs average losses of about 4.5 percent (VIcore) of its capital from failures in the core network (paragraph 47).
  - Covered bonds contribute the largest share to core network’s vulnerabilities, followed closely by unlisted shares. Considerable deposit-related losses for MCIs partly due to a temporary spike in their deposits observed on September 30, 2019 (paragraph 47).
- Overall versus core vulnerability:
  - Considering the full network, systemic banks face the highest inward spillover losses (paragraph 47).
  - Overall vulnerability indices are significantly lower (about one to ten) than core vulnerability indices due to dilutive effect of increasing network size from 21 to 1005 nodes (paragraph 47).
  - Systemic banks’ average overall vulnerability index is three times higher than that of MCIs when full network is considered (paragraph 47).
- Loss attribution from outside core:
  - Significant portion of systemic and non-systemic banks’ losses from outside the core network attributable to loans, deposits and other claims — likely credit exposures to households and NFCs and residual group “Other”, including OFIs and interbank deposits held at non-core, including foreign, credit institutions (paragraph 47).
  - MCIs have large exposures to households and NFCs, but these do not create contagion losses due to extremely low LGD values associated with these exposures. MCIs are less vulnerable to shocks from outside the banking system unless there is a significant drop in real estate prices impacting collateral values and raising LGD (paragraph 47).

### Cascade Effects and Risk Map
- Two types of cascade effects distinguished (paragraph 48):
  - Repricing channel: captures market reaction to losses from credit and funding channels and moves gradually.
  - Knock-on effects: occur when counterpart reaches default threshold and causes contagion losses to others.
- Findings:
  - Amplified losses through repricing channel are limited, partly due to data characteristics: covered bonds have shorter durations and very high initial credit ratings (AAA) with uplift buffers, resulting in relatively small valuation losses solely due to credit spreads (paragraph 48).
  - Knock-on effects and subsequent-round losses are similarly small; low number of contagion defaults observed, defaults associated with smaller non-systemic banks or intra-group entities (paragraph 48).
- Risk Map:
  - Identifies four entities relatively high on both contagion and vulnerability indices — critical zone where entities are both more exposed to contagion risks and can amplify spillovers (paragraph 49).
  - Risk Map plots normalized CI and VI (between 0 and 1); entities in dark-shaded quadrant are relatively both more contagious and more vulnerable (Figure notes, paragraph 49).

*Source: Supervisory data; IMF staff calculations. Content based on supplied IMF Technical Note excerpts.*

### 50.      This section tests the sensitivity of the main findings to a range of parameter

### 1dnkea2020007 - 50.      This section tests the sensitivity of the main findings to a range of parameter

### Rating Conversion and Migration
- Baseline calibration: macro environment assessed as "moderate" (see Methodology).
- Two alternative assumptions tested:
  - Stronger assumption: based on “weak” macro profile — a given capital adequacy ratio corresponds to a lower credit rating, so the same decline in the ratio provokes a larger yield change in the issuer’s securities.
  - Milder assumption: based on “strong” macro profile — a given capital adequacy ratio corresponds to a higher credit rating, so yield changes are smaller.
- Key finding:
  - Little sensitivity to assumptions around market reaction to changes in banks’ capital adequacy.
  - Alternative assumptions do not generate material variation in contagion and vulnerability indices; ranking of entities by contagiousness and vulnerability hardly changes.
  - Explanation: small share of contagion losses associated with market pricing mechanism.

### Funding Shortfall Ratio
- Alternative assumption: raise maturity related to calculation of short-term funding from one month to three months.
  - Rationale: more stringent assumption should increase funding withdrawals and fire-sale losses.
- Key findings:
  - No additional contagion losses when funding shortfall amount is raised.
  - Explanation: banks’ ability to use liquidity buffers to withstand further tightening in funding.
  - Observed effect: average increase in liquidity received through central bank credit facility (DN Credit Facility) in percent of NLO.

### Default Ratio for Households and NFCs
- Approach: households and NFCs aggregated at sector/industry level; main exercise uses a “default ratio” parameter to represent portion of these sectors defaulting on loans.
- Sensitivity test design:
  - Default ratio increased in 5 percentage point increments up to 100 percentage points to detect tipping points and non-linearities.
  - Note: default rate and loss-given-default (LGD) enter multiplicatively to determine losses on an exposure.
- Illustrative combinations:
  - If LGD for household loans = 2 percent, a 100 percent default rate → 2 percent losses on this exposure.
  - That 2 percent loss corresponds to 50 percent default ratio if LGD = 4 percent, or 10 percent default ratio if LGD = 20 percent.
- Key findings:
  - Household and Real Estate sectors’ contagion losses are almost entirely linear with respect to default rate.
  - A few kinks reflect defaults of individual entities as they fail, but slopes remain stable.
  - Implication: no tipping points detected that would increase the speed and extent of cascade effects.

### Default Threshold
- Alternative: raise default threshold from minimum CET1 to include all regulatory buffers.
  - Banks are subject to three regulatory buffer requirements: capital conservation buffer (2.5 pct), SIFI buffer (0-3 pct), and countercyclical capital buffer (1-1.2 pct).
  - Breaching buffers does not lead to default but imposes restrictions (e.g., dividend payments, interest on hybrid instruments) that can weaken access to external funding.
  - Entity-specific buffer levels used to reflect heterogeneity across banks.
- Key findings:
  - Overall contagion losses experienced by each bank increase when threshold includes buffers.
  - Ranking of entities changes noticeably; in some cases an entity previously in the lower half becomes one of the top 3 with its contagion index almost tripling.
  - Changes in entities causing contagion are fewer but more significant in magnitude.

### Overall Robustness of Findings
- Findings broadly robust to a number of alternative assumptions and calibrations.
- No significant non-linearities observed for incremental changes, except for default threshold where setting threshold in line with bank-specific required buffers leads to significant changes in absolute and relative contagion losses.

### Caveats and Limitations
- Repricing channel modeled captures changes in market valuation due only to credit spreads driven by capitalization.
  - Additional contagion from market liquidity shocks (e.g., selling pressures in covered bonds) not incorporated due to data limitations; inclusion would likely increase overall contagion and the role of repricing channel.
- Single datapoint used: September 30, 2019.
  - On that date MCIs experienced very high liquidity due to large mortgage refinancing flows; these deposits were temporary and used to pay investors on October 1, 2019.
  - As a result, losses due to deposit exposures could be overestimated and asymmetrically distributed across entities.
- Aggregation and sector treatment:
  - Danish OFIs, investment funds, governmental entities and cross-border exposures aggregated and treated as sector-level nodes; trigger shock implies default of the entire sector since shocks are not parametrized with a default rate for these nodes.
- Solo-level analysis:
  - Financial entities considered at solo level reflecting reporting, but largest Danish SIFIs are groups (CI, MCI, subsidiaries). Group structure causes mother companies to incur large losses through intra-group unlisted share ownership when a subsidiary defaults.
  - For core network, ~90 percent of unlisted shares represent intra-group ownership; for full network ~75 percent.
- Data gaps:
  - Analysis largely based on banks' reporting. Securities data complement some gaps but significant gaps remain (e.g., non-bank wholesale funding exposures, foreign ownership of securities, balance sheets of non-bank and foreign financial entities).
  - Partial coverage of outward spillovers may underestimate contagion risks, given potential feedback loops with Nordic and EA banking sectors.

### Conclusion and Policy Implications
- Main results:
  - Risk of contagion strongest within the banking system due to intra-group exposures and cross-ownership of covered bonds.
  - MCIs are a key source of potential contagion.
  - Systemic banks have a higher vulnerability index than MCIs and non-systemic banks; their vulnerability stems from within the banking system and from other sectors of the economy.
  - Credit channel is the primary channel propagating contagion losses.
  - Nordic region and EA banking systems are significant sources of cross-border spillovers to Denmark.
- Recommendations / implications:
  - Critical to map all interlinkages of the covered bond market and model transmission through different financial intermediaries and the real sector.
  - Close data gaps and develop a more comprehensive analytical framework to study contagion risks to and from the Danish financial system.
  - Strengthen overall macroprudential stress-testing framework by incorporating contagion effects across financial institutions.

*Source: Supervisory data; IMF staff calculations; single datapoint: September 30, 2019.*

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_Source: https://www.imf.org/-/media/files/publications/cr/2020/english/1dnkea2020007.pdf_