## _wp09257

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### Global financial crisis and policy responses
- The crisis followed the bursting of the credit boom and housing bubble in the United States and has been characterized by a vicious self-reinforcing mechanism of deleveraging, tightened financial conditions, asset prices deflation, and output losses.
- Central banks in major economies, particularly the Fed, have:
  - lowered their policy rates to near zero;
  - introduced measures aimed at increasing liquidity and stimulating credit in domestic markets, including serving as lender of last resort for systemically important institutions, creating new central bank facilities, and buying government or corporate securities.1
- These measures have somewhat alleviated pressure in credit markets, but the persistence of the global financial crisis and the magnitude of losses that financial and non-financial institutions around the world have incurred illustrate the importance of macro-financial interlinkages.
- Greater trade and financial integration have heightened contagion risks for macroeconomic and financial stability.

### Trade-offs of accommodative policy stances
- The accommodative monetary policy stances in the bulk of the world economy, combined with forceful fiscal policy responses worldwide, have:
  - helped ease the extent of the downturn and facilitate a process of economic recovery;
  - created a risk that an early withdrawal of macroeconomic stimulus could put at risk the nascent global recovery.
- Conversely, protracted easy monetary and fiscal conditions could create inflation in goods and assets markets, risking future macroeconomic and financial stability.

### Modeling approach and innovations
- The paper analyzes the potential macroeconomic benefits of adopting countercyclical macro prudential rules to mitigate risks of asset price inflation while safeguarding the recovery in the real economy.
- The analysis uses a model that integrates forward-looking indicators of balance sheet risk into a traditional multicountry model for monetary analysis to better capture interlinkages between the financial sector and the real sector (see Gray, Karam, and N’Diaye (2009)).
- The modeling strategy follows the tradition of the financial accelerator process pioneered by Bernanke, Gertler, and Gilchrist (1999).
- Borrowing costs depend on an “external finance premium” or a spread that reflects borrowers net worth.
- Distinct from other approaches, the external finance premium is modeled drawing on the contingent claims analysis (CCA), commonly called the Merton Model.3
  - This CCA approach helps better capture underlying risk and interactions between balance sheets, where financial distress at the corporate or household level affects banks’ balance sheets, which in turn feeds back into the real sector—a mechanism not present in standard financial accelerator frameworks.2

### Key simulation results and insights
- Simulation results suggest that countercyclical prudential regulations, when binding, can:
  - help reduce output fluctuations;
  - reduce the risks of financial instability.
- With countercyclical regulatory rules—such as countercyclical capital adequacy ratios—central banks can achieve the same objectives in terms of output and inflation but with less adjustment in policy interest rates.
- Countercyclical capital adequacy rules can help stem swings in asset prices.
- Given that rapid asset price increases combined with high credit growth have been found to be key ingredients in the making of financial disasters,4 countercyclical macro prudential rules could have the potential to lessen the risks of financial instability.

### Overview of the Contingent Claims Approach (CCA)
- The CCA combines balance sheet information with finance and risk management tools to construct marked-to-market balance sheets that better reflect underlying risk.
- Basis: liabilities derive their value from asset values that serve as collateral; collateral asset values are stochastic and can move relative to promised payments, creating a risk of financial distress.
- Default definition (practical): assets fall below the “distress barrier” defined as all short-term debt, a fraction of long-term debt, and one year of interest payments.
- The distress risk (probability of default) is estimated using option pricing tools; the guarantee against default is modeled as a put option on the assets with exercise price equal to the value of the debt.
- Distinction between actual and risk-adjusted (risk-neutral) probability distributions:
  - The risk-adjusted (risk-neutral) distribution substitutes the risk-free interest rate r for the actual expected return μ.
  - The “risk-adjusted” probability of default is larger than the actual probability of default for assets with μ greater than r.
- Formal relationships summarized in equations (1)–(6), including:
  - Assets = Equity + Risky Debt (equation (1))
  - Risky Debt = Default-Free Debt − Debt Guarantee (equation (2))
  - Probability of default PD = Nd(−d) per equation (5)
  - Spread formula in equation (6)
- CCA is well suited to analyze balance sheet effects, including how spreads/external finance premium increase with asset volatility, maturity and currency mismatches, funding difficulties, interest rate and exchange rate changes, shocks to asset returns, shocks to GDP growth and employment, and the feedback loops among these.

### Balance Sheet Dynamics, Liquidity, and Tail Risk
- Funding liquidity and rollover options affect the effective distress barrier:
  - In calm periods with easy funding liquidity, short-term debt can be rolled over and the effective default barrier is lower (lower PD, very low spread).
  - In crisis periods, assets may be illiquid and subject to sharp discounts (fatter left tail), and inability to roll over debt raises the distress barrier (higher PD, much higher credit spreads).
- Illiquidity increases the probability of large declines in asset values (fatter tail) and raises credit spreads.

### Model Overview and Key Mechanisms
- The multi-country macroeconomic model integrates standard macro elements (IS curve, Phillips curve, Okun’s law, monetary rule, yield curve, modified UIP, labor income relationship) with CCA-based financial sector equations (equations (1)–(6)) tailored to three sectors: corporates, households, and banks; accommodates up to 4 economies.
- Monetary policy (policy rate) transmits via short-term market rates and a modified uncovered interest parity to exchange rates, which affect aggregate demand and inflation; short-term market rates affect long-term rates via the yield curve.
- Balance sheets of corporates, households, and banks are affected by policy rate, market interest rates, exchange rates, output and unemployment gaps, inflation, and asset prices, generating feedback loops between real and financial sectors.
- Financial regulation in the model:
  - Households and corporates face loan-to-value limits.
  - Banks face capital adequacy ratio limits (equity over assets); banks’ capital requirements move with the economic cycle and are a function of the output gap.
- Key financial sector constructs:
  - Sectoral asset market values are present discounted sums of future profits/dividends/rents/labor income (see corporate, household, bank asset equations).
  - Asset volatilities derived from equity volatility via Black-Scholes relationship (equation (26)).
  - Aggregate spread is a weighted average of sectoral spreads, defined following equation (6) and specified in equation (18), with implicit guarantees GU, FGU, RGU defined in equation (19).
- Debt dynamics distinguish short-term and long-term debt, domestic and foreign currency denominations (equations (28)–(31)).
- Financial regulations govern the contracting of new debt (ND) and impose limits via capital and loan-to-value constraints (equations (32)–(33)).
- Equity values are assets net of risky debt (equations (34)–(35)).
- Supply side is rudimentary: variables modeled as deviations from equilibrium and follow simple stochastic processes; trends measured using the LRX filter.

### Illustrative Model Simulations — Role of Countercyclical Prudential Regulations
- Simulation scenario: an exogenous expansion of domestic demand for a couple of quarters, compare paths with and without countercyclical prudential regulations.
- Propagation mechanism of a demand boom:
  - Higher domestic demand raises corporate profits and corporate asset values → increases collateral → lowers corporate credit risk → reduces firms’ borrowing costs.
  - Higher demand raises household income and lowers unemployment → increases household asset values and lowers household credit risk → reduces household financing costs.
  - Overall financial conditions ease, but higher inflation risk may prompt monetary tightening.
- Effects without countercyclical regulations: banks expand lending, fueling larger increases in asset prices and collateral (stronger financial accelerator).
- Effects with countercyclical capital rules:
  - Banks required to hold more “hybrid” debt to meet higher capital requirements during booms; this dilutes bank equity and raises banks’ borrowing costs.
  - Tighter financial conditions slow output increases, temper asset price rises during booms (and reduce asset price declines during downturns).
  - Result: smaller required adjustments in interest rates by monetary authorities to achieve the same objectives in terms of deviations of output and inflation from targets.
  - In fixed exchange rate regimes, tighter regulatory requirements could lessen inflationary pressures in goods and asset markets and lower output fluctuations.
- Quantitative/qualitative simulation outcomes:
  - Countercyclical prudential regulations can lower output fluctuations and alleviate the burden on monetary authorities.
  - Capital adequacy rules, when binding, stem increases in asset prices in booms and limit asset price drops in downturns, lowering risks of financial instability.
  - Asset prices in the model tend to move with a greater amplitude than CPI due to their more forward-looking nature and lower stickiness.

### Policy Conclusions and Implementation Challenges
- Main conclusion: countercyclical macroprudential rules (e.g., countercyclical capital adequacy rules) can support monetary policy in reducing output fluctuations while maintaining financial stability.
- Specific policy implications:
  - With binding countercyclical regulatory rules, monetary authorities can achieve the same objectives for output and inflation with smaller interest-rate adjustments.
  - Countercyclical capital adequacy rules help mitigate swings in asset prices and potentially lower the risks of financial instability.
- Implementation caveats:
  - Appropriately calibrating countercyclical macroprudential rules to individual country circumstances may be complex.
  - Calibration is particularly challenging where banks already exceed existing capital adequacy requirements.

*Source: _wp09257 — Sections: References; Section V concludes; Overview of the Contingent Claims Approach; Model; Illustrative Simulations; Policy Conclusions.*

### References..............................................................................................................

### References — Introduction (excerpt)

### Global financial crisis and policy responses
- The crisis followed the bursting of the credit boom and housing bubble in the United States and has been characterized by a vicious self-reinforcing mechanism of deleveraging, tightened financial conditions, asset prices deflation, and output losses.
- Central banks in major economies, particularly the Fed, have:
  - lowered their policy rates to near zero;
  - introduced measures aimed at increasing liquidity and stimulating credit in domestic markets, including serving as lender of last resort for systemically important institutions, creating new central bank facilities, and buying government or corporate securities.1
- These measures have somewhat alleviated pressure in credit markets, but the persistence of the global financial crisis and the magnitude of losses that financial and non-financial institutions around the world have incurred illustrate the importance of macro-financial interlinkages.
- Greater trade and financial integration have heightened contagion risks for macroeconomic and financial stability.

### Trade-offs of accommodative policy stances
- The accommodative monetary policy stances in the bulk of the world economy, combined with forceful fiscal policy responses worldwide, have:
  - helped ease the extent of the downturn and facilitate a process of economic recovery;
  - created a risk that an early withdrawal of macroeconomic stimulus could put at risk the nascent global recovery.
- Conversely, protracted easy monetary and fiscal conditions could create inflation in goods and assets markets, risking future macroeconomic and financial stability.

### Modeling approach and innovations
- The paper analyzes the potential macroeconomic benefits of adopting countercyclical macro prudential rules to mitigate risks of asset price inflation while safeguarding the recovery in the real economy.
- The analysis uses a model that integrates forward-looking indicators of balance sheet risk into a traditional multicountry model for monetary analysis to better capture interlinkages between the financial sector and the real sector (see Gray, Karam, and N’Diaye (2009)).
- The modeling strategy follows the tradition of the financial accelerator process pioneered by Bernanke, Gertler, and Gilchrist (1999).
- Borrowing costs depend on an “external finance premium” or a spread that reflects borrowers net worth.
- Distinct from other approaches, the external finance premium is modeled drawing on the contingent claims analysis (CCA), commonly called the Merton Model.3
  - This CCA approach helps better capture underlying risk and interactions between balance sheets, where financial distress at the corporate or household level affects banks’ balance sheets, which in turn feeds back into the real sector—a mechanism not present in standard financial accelerator frameworks.2

### Key simulation results and insights
- Simulation results suggest that countercyclical prudential regulations, when binding, can:
  - help reduce output fluctuations;
  - reduce the risks of financial instability.
- With countercyclical regulatory rules—such as countercyclical capital adequacy ratios—central banks can achieve the same objectives in terms of output and inflation but with less adjustment in policy interest rates.
- Countercyclical capital adequacy rules can help stem swings in asset prices.
- Given that rapid asset price increases combined with high credit growth have been found to be key ingredients in the making of financial disasters,4 countercyclical macro prudential rules could have the potential to lessen the risks of financial instability.

### Paper organization (excerpt)
- Section II gives an overview of the CCA.
- Section III presents the model.
- Section IV presents an illustrative scenario that highlights the potential role of macro prudentials in stabilizing output and promoting financial stability.

*Source: _wp09257 - References*

### Section V concludes.

### Section V concludes.

### Overview of the Contingent Claims Approach (CCA)
- The CCA combines balance sheet information with finance and risk management tools to construct marked-to-market balance sheets that better reflect underlying risk.
- Basis: liabilities derive their value from asset values that serve as collateral; collateral asset values are stochastic and can move relative to promised payments, creating a risk of financial distress.
- Default definition (practical): assets fall below the “distress barrier” defined as all short-term debt, a fraction of long-term debt, and one year of interest payments.
- The distress risk (probability of default) is estimated using option pricing tools; the guarantee against default is modeled as a put option on the assets with exercise price equal to the value of the debt.
- Distinction between actual and risk-adjusted (risk-neutral) probability distributions:
  - The risk-adjusted (risk-neutral) distribution substitutes the risk-free interest rate r for the actual expected return μ.
  - The “risk-adjusted” probability of default is larger than the actual probability of default for assets with μ greater than r.
- Formal relationships summarized in equations (1)–(6), including:
  - Assets = Equity + Risky Debt (equation (1))
  - Risky Debt = Default-Free Debt − Debt Guarantee (equation (2))
  - Probability of default PD = Nd(−d) per equation (5)
  - Spread formula in equation (6)
- CCA is well suited to analyze balance sheet effects, including how spreads/external finance premium increase with asset volatility, maturity and currency mismatches, funding difficulties, interest rate and exchange rate changes, shocks to asset returns, shocks to GDP growth and employment, and the feedback loops among these.

### Balance Sheet Dynamics, Liquidity, and Tail Risk
- Funding liquidity and rollover options affect the effective distress barrier:
  - In calm periods with easy funding liquidity, short-term debt can be rolled over and the effective default barrier is lower (lower PD, very low spread).
  - In crisis periods, assets may be illiquid and subject to sharp discounts (fatter left tail), and inability to roll over debt raises the distress barrier (higher PD, much higher credit spreads).
- Illiquidity increases the probability of large declines in asset values (fatter tail) and raises credit spreads.

### Model Overview and Key Mechanisms
- The multi-country macroeconomic model integrates standard macro elements (IS curve, Phillips curve, Okun’s law, monetary rule, yield curve, modified UIP, labor income relationship) with CCA-based financial sector equations (equations (1)–(6)) tailored to three sectors: corporates, households, and banks; accommodates up to 4 economies.
- Monetary policy (policy rate) transmits via short-term market rates and a modified uncovered interest parity to exchange rates, which affect aggregate demand and inflation; short-term market rates affect long-term rates via the yield curve.
- Balance sheets of corporates, households, and banks are affected by policy rate, market interest rates, exchange rates, output and unemployment gaps, inflation, and asset prices, generating feedback loops between real and financial sectors.
- Financial regulation in the model:
  - Households and corporates face loan-to-value limits.
  - Banks face capital adequacy ratio limits (equity over assets); banks’ capital requirements move with the economic cycle and are a function of the output gap.
- Key financial sector constructs:
  - Sectoral asset market values are present discounted sums of future profits/dividends/rents/labor income (see corporate, household, bank asset equations).
  - Asset volatilities derived from equity volatility via Black-Scholes relationship (equation (26)).
  - Aggregate spread is a weighted average of sectoral spreads, defined following equation (6) and specified in equation (18), with implicit guarantees GU, FGU, RGU defined in equation (19).
- Debt dynamics distinguish short-term and long-term debt, domestic and foreign currency denominations (equations (28)–(31)).
- Financial regulations govern the contracting of new debt (ND) and impose limits via capital and loan-to-value constraints (equations (32)–(33)).
- Equity values are assets net of risky debt (equations (34)–(35)).
- Supply side is rudimentary: variables modeled as deviations from equilibrium and follow simple stochastic processes; trends measured using the LRX filter.

### Illustrative Model Simulations — Role of Countercyclical Prudential Regulations
- Simulation scenario: an exogenous expansion of domestic demand for a couple of quarters, compare paths with and without countercyclical prudential regulations.
- Propagation mechanism of a demand boom:
  - Higher domestic demand raises corporate profits and corporate asset values → increases collateral → lowers corporate credit risk → reduces firms’ borrowing costs.
  - Higher demand raises household income and lowers unemployment → increases household asset values and lowers household credit risk → reduces household financing costs.
  - Overall financial conditions ease, but higher inflation risk may prompt monetary tightening.
- Effects without countercyclical regulations: banks expand lending, fueling larger increases in asset prices and collateral (stronger financial accelerator).
- Effects with countercyclical capital rules:
  - Banks required to hold more “hybrid” debt to meet higher capital requirements during booms; this dilutes bank equity and raises banks’ borrowing costs.
  - Tighter financial conditions slow output increases, temper asset price rises during booms (and reduce asset price declines during downturns).
  - Result: smaller required adjustments in interest rates by monetary authorities to achieve the same objectives in terms of deviations of output and inflation from targets.
  - In fixed exchange rate regimes, tighter regulatory requirements could lessen inflationary pressures in goods and asset markets and lower output fluctuations.
- Quantitative/qualitative simulation outcomes:
  - Countercyclical prudential regulations can lower output fluctuations and alleviate the burden on monetary authorities.
  - Capital adequacy rules, when binding, stem increases in asset prices in booms and limit asset price drops in downturns, lowering risks of financial instability.
  - Asset prices in the model tend to move with a greater amplitude than CPI due to their more forward-looking nature and lower stickiness.

### Policy Conclusions and Implementation Challenges
- Main conclusion: countercyclical macroprudential rules (e.g., countercyclical capital adequacy rules) can support monetary policy in reducing output fluctuations while maintaining financial stability.
- Specific policy implications:
  - With binding countercyclical regulatory rules, monetary authorities can achieve the same objectives for output and inflation with smaller interest-rate adjustments.
  - Countercyclical capital adequacy rules help mitigate swings in asset prices and potentially lower the risks of financial instability.
- Implementation caveats:
  - Appropriately calibrating countercyclical macroprudential rules to individual country circumstances may be complex.
  - Calibration is particularly challenging where banks already exceed existing capital adequacy requirements.

*Source: _wp09257 - Section V concludes.*

### References

### References

### Monetary policy, asset prices, and uncertainty
- Bernanke, B., 2002, “Asset-Price ‘Bubbles’ and Monetary Policy,” remarks before the of the National Association for Business Economics , New York Chapter, October.
- Bernanke, B., M. Gertler, and S. Gilchrist, 1999, “The Financial Accelerator in a Quantitative Business Cycle Framework,” in Handbook of Macroeconomics, ed. by J. Taylor and M. Woodford (Amsterdam: Elsevier).
- Greenspan, Alan, 2004, “Risk and Uncertainty in Monetary Policy,” American Economic Association Papers and Proceedings, Vol. 94, No. 2, pp. 33–40.
- Selody, J, and C. Wilkins, 2004, “Asset Prices and Monetary Policy: A Canadian Perspective On The Issues,” Bank of Canada Review, Vol. 2004 (Autumn), pp. 3–14..
- Hunt, B., and A. Orr, 1999, “Monetary Policy Under Uncertainty,” Reserve Bank of New Zealand Conference (Wellington: Reserve Bank of New Zealand).
- Hunt, B., P. Isard, and D. Laxton, 2003, “Inflation Targeting and the Role of the Exchange Rate,” (unpublished; Washington: International Monetary Fund).

### Macrofinancial risk, financial stability, and banking crises
- Borio, C and M Drehmann (2009) “Assessing the risk of banking crises – revisited”, BIS Quarterly Review, March, pp. 29-46.  
- Gray, Dale, and Samuel Malone, 2008, “Macrofinancial Risk Analysis,” (West Suxxex: Wiley Finance).
- Gray, D., R. C. Merton, and Z. Bodie, 2008, “A New Framework for Measuring and Managing Macrofinancial Risk and Financial Stability,” Harvard Business School WP 09-015.
- Kiyotaki, N., and J. Moore, 1997, “Credit Cycles,” Journal of Political Economy, Vol. 105, pp. 211–48.

### Modeling, policy analysis, and practical guides
- Blanchard, O., and J. Gali, 2006, “A New Keynesian Model with Unemployment,” draft, National Bureau of Economic Research.
- Berg, A., P. Karam, and D. Laxton, 2006, “Practical Model-Based Monetary Policy Analysis—A How-To Guide,” IMF Working Paper 06/81 (Washington: International Monetary Fund).
- Karam, P, D. Gray, and P. N’Diaye, 2009, “Integrating Macro-Financial Sector Analysis,” forthcoming, IMF Working Paper (Washington: International Monetary Fund).
- Taylor, J, ed., 1999, Monetary Policy Rules (Chicago: University of Chicago Press).

### Option-pricing theory and applications
- Merton, R.C. , 1998, “Applications of Option-Pricing Theory: Twenty-Five Years Later,” Les Prix Nobel 1997, Stockholm: Nobel Foundation; reprinted in American Economic Review, Vol. 88 (June), pp. 323–49.

*Document: _wp09257 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09257.pdf_