## Factor Model for Stress-Testing with a Contingent Claims Model of the Chilean Banking SystemThis paper derives risk indicators for the major Chilean banks based on contingent claims analysis, an extension of Black-Scholes-Merton option-pricing theory. These risk indicators are clearly tied to macroeconomic and financial developments in Chile and outside, but bank responses are highly heterogeneous. To reduce the number of variables linked to the banks'' risk to a tractable number, we apply principal component analysis. Vector autoregressions of risk indicators with the most significant factors show strong ties from financial markets and regional developments. Impulse response functions from these factors are derived, which allow for scenario testing. The scenarios derived in the paper illustrate how the magnitude and persistence of responses of bank credit risk can vary across banks in the system. |

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### Contents

I Introduction | 3 |

II Risk Measures from Contingent Claims Analysis | 4 |

Figures | 6 |

III Relating Default Risk to Macroeconomic Variables | 14 |

Tables | 15 |

IV Areas for Further Research | 27 |

V Conclusions | 29 |

References | 31 |

Annex | 34 |

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### Common terms and phrases

assessing asset retum Asset Value assumption balance sheets bank assets bank risk bank’s banking sector risk banks show Brazilian presidential elections Brazilian real calculated calibrate capital adequacy CCA model Central Bank changes Chile CONTINGENT CLAIMS ANALYSIS correlated credit risk crisis cyclical factors cyclical variables default barrier derived developments in financial Distance to Default distance to distress distance-to-distress distress barrier domestic/regional effect factor is significant factor loadings Figure financial institutions financial markets financial-market financials factor four factors held by banks IMF Working Paper impulse response International Monetary Fund lags larger banks macro variables macroeconomic variables market capitalization Merton Model percent price of risk principal component analysis probability of default promised payments put option risk measures risk-adjusted risk-free interest rate risk-free rate risk-neutral default probability risky debt sample scenario Scenario Testing smaller banks stepwise regressions strongly U.S. interest rates U.S. yield curve value of assets volatility measure