Abstract
I discuss how the influence of outstanding debt on financial crises occurrence and the relationship between different types of crises can be modeled using a stochastic and dynamic framework in continuous time and (compound-) option theory. This approach especially enables us to consider the influence of the debt’s maturity and the uncertainty about the amount of funds the government is able and willing to spend for crisis avoidance. It can be shown that this uncertainty increases crisis risk in most situations. The risk of a financial crisis is higher with (higher) outstanding debt repayments. A shorter maturity of debt increases crisis risk.
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Notes
- 1.
The term “quasi-default” refers to a situation where a country required international help to fulfill its debt service obligations.
- 2.
- 3.
An important deterministic and theoretic approach to country default risk analyzes the determinants of a country’s willingness to pay, i.e. the pros and cons of debt repayment or default. See Eaton et al. (1986) or Eaton and Fernandez (1995) for an overview. Another strand of the theoretical debt crisis literature focuses on a country’s ability to pay, i.e. the amount of funds a country is able to spend for debt servicing. Examples are Avramovic et al. (1964) and Diaz-Alejandro (1984).
- 4.
The explanations also hold true for the occurrence of a default, if we consider an indebted country with outstanding debt obligations payable at only one point in time where the banking system is sound. This is the typical situation considered in the default risk models mentioned in the introduction.
- 5.
Whereas we focus on banking crises also currency crises could be considered in our framework: for a country without outstanding debt service payments B1 describes the amount of funds required to fend off an attack on the currency (plus the funds required to bail-out the banking sector – as the case may be). The government avoids a financial crisis by exchanging foreign currency (and/or bailing out the banking sector), if the state variable W is higher than the required funds; otherwise, it faces a financial crisis. If the payments for avoiding the currency crisis and the banking crisis are required at different dates, this could be captured by the general (multi-payment) framework developed in Sect. 2.3.
- 6.
We make this assumption to simplify the explanations. We later generalize our model, allowing an arbitrary number of later payment dates.
- 7.
If, for example, the amount of funds required for the bailout is USD 10 billion and USD 10.01 billion is available but USD 5 billion is due at the next payment date, the government may refuse to bail out the banking system since it will face a financial crisis no matter what and can save the USD 10 billion.
- 8.
All papers that use structural credit risk models to analyze country default risk or bank failures and bank deposit insurance rely on these assumptions (see the discussion in the introduction). Certain default risky debt instruments, such as government bonds, can be combined with corresponding credit default swaps to diversify default risk.
- 9.
- 10.
The influence of the time span on the threshold can be seen in Fig. 3 when comparing the three solid lines (or the dashed lines) with each other.
- 11.
In addition to the short-term payments required to avoid a crisis, B1, the threshold also depends on the current value, F2, of the long-term payments, B2 (see Eq. 5). The value of F2 depends on the volatility (see Eq. 6). For higher long-term payments, the volatility has a stronger impact on the threshold WQ, ceteris paribus.
- 12.
Such a situation may occur especially when the state variable at the date of prognosis is comparatively low and the drift high. Situations where the short-term payments are high compared to the long-term payments also lead by tendency to these differences in the influence on short-term and long-term risk.
- 13.
Such a situation prevails, for example, when the current value of the state variable is high and the drift is negative or when short-term payments are low and long-term payments are high.
- 14.
Both the short-term and long-term payments are set to one, and the time span between payments is assumed to be three years. The risk-less interest rate is 5 %. The resulting (volatility depending) short-term thresholds are shown in Fig. 3 by the solid line market with squares. The day of prognosis, t, is one year before the first crisis date, T1.
- 15.
An empirical application could quantify the model’s parameters based on observable market data, such as prices of financial instruments, as is done, e.g., in some of the single-crisis stochastic models mentioned in the introduction.
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Maltritz, D. (2013). Financial Crises and Sovereign Default: Dependencies, Timing and Uncertainty in a Stochastic Framework. In: Maltritz, D., Berlemann, M. (eds) Financial Crises, Sovereign Risk and the Role of Institutions. Springer, Cham. https://doi.org/10.1007/978-3-319-03104-0_8
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