Appendix I. Extensions of the Merton Model
Appendix II. Regression Results of Output and Output Gap on Distance-to-Default of the Banking System
Appendix III. Extensions and Further Applications
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Mr. Gray is a Senior Risk Expert in the Monetary and Capital Markets Department, IMF. Mr. García is a professor at ILADES-Universidad Alberto Hurtado. Mr. Luna works for Transelec, Chile. Mr. Restrepo is a senior economist in the IMF Institute. Most of this article was written while Mr. Restrepo was a senior economist at the Central Bank of Chile. We thank Rodrigo Alfaro, Nicolas Magud, Jorge Chan-Lau, Jonathan Wright, as well as the participants at a Central Bank of Chile’s conference and an IMF seminar. All errors are the authors’ own.
The term FSI used here is an indicator derived from forward-looking market information, including indicators from the CCA model. This should not be confused with the accounting ratio financial stability indicators.
An alternative could also be designed in which the central bank only reacts directly to financial risk whenever financial stability indicator breaches a predetermined threshold.
Bernanke, Gertler, and Gilchrist (1999) introduced financial frictions into a business cycle model. The relation of monetary policy and financial stability is discussed in Walsh (2009) and the literature surveyed therein.
The authors would like to thank Jonathan Wright for this observation.
On the other hand, very large dtd could reflect bubbles in asset prices, which usually have bitter endings.
See Merton (1992, pp. 334–343; 448–450).
The CCA framework is an extension of Merton’s models of risky debt (1974) and deposit insurance (1977).
This has not been the case for many banks in the last sub-prime crisis.
For simplicity, we did not consider explicitly the volatility of foreign debt. In Chile, bank’s foreign debt in the analyzed period represented only 7 percent of total debt.
A linear transformation of the balance sheet data is performed in order to get daily data.
Echeverría, Gómez, and Luna (2008) include a detailed analysis of measuring distance-to-default, in which they consider alternative strategies to obtain direct volatility.
Tudela and Young (2003) find that the distance-to-default measure anticipates changes in the risk ratings of banks in Europe. Moody’sKMV CreditEdge model uses this framework to estimate daily default probabilities for 35,000 corporations and financial institutions worldwide and their research shows very good predictive power of the CCA based indicators.
As already said, The CCA risk indicators shown in Figure 3 are taken from Gray, Echeverría, and Luna (2006), who used daily market capitalization for the banks obtained by the Central Bank of Chile from the Bolsa de Santiago. Bank debt was obtained from the Central Bank of Chile’s database. Financial practitioners use various methods for estimating the volatility of daily asset returns. Two frequently used methods model daily volatility either as a GARCH(1,1) or as a moving average process. The GARCH(1,1) methodology for all banks in the sample was used in this case, but the results of the moving-average model are similar.
As we see below, this leveling-off has occurred at a very low level of risk.
A related issue is whether an indicator of market risk appetite such as the VIX should be included in monetary policy models along with the risk indicator. This could help estimate the impact of the credit risk indicator on the GDP gap, adjusted for changes in risk appetite. Also, risk indicators for a group of institutions could include the correlation, or dependence, structure observed between the institutions.
There are several other interesting routes to take in linking risk analytics more closely with macroeconomic models. These include incorporating default risk and a risk premium into the Mundell-Fleming model to separate out the effects of changes in interest rates due to changes in the market for liquidity, and changes in interest rates due to changes in the risk premium on debt (see Gray and Malone, 2009).
Dynare has an explicit function built in for the cumulative normal distribution function.
It is worth mentioning that the spread put is another measure of risk that could be used alternatively. It is described in Gray, Merton and Bodie (2008) and Gray and Malone (2008) as a function of the value of the Put option, the default barrier, the risk free rate and time: spread _put = −1/t*log (1− PUT/BB*exp(−r * t)) −0.00925382 Even though the spread put is a useful concept, it was not used in the simulations performed with the model here.
A not reported negative shock to distance-to-default causes an initial small drop in ygap. However, due to the fact that dtd is included in the policy reaction function, the original shock is followed by a reduction in the MPR. Moreover, arbitrage through the uncovered interest parity as well as the respective hike of the risk premium result in a large real depreciation. Thus, the interest rate and the exchange rate fuel a GDP expansion.
See Papa N’Diaye, Countercylical Macroprudential Policies in a Supporting Role to Monetary Policy, 2009.