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Robert Merton’s Approach for Macrofinancial Risks 罗伯特·默顿的主权信用风险模型

Traditional Macrofinancial framework vs. Robert Merton’s Macrofinancial Framework

The traditional approach to measure sovereign credit risk is based upon the assessment of a country’s ability and willingness to service its debt, which takes into account key economic, socio-political, global market, and governance attributes of sovereign entities.

Robert C. Merton proposed an alternative approach in this regard. He utilizes the natural framework of contingent claims analysis (CCA) and demonstrates that when considering sovereign risk, policy, monetary, fiscal, and financial stability should be integrated. In another word, the belief of this approach is that banks, insurance companies, and sovereign entities are dynamically connected, with one country spreading risk to another.

The Robert Merton Approach

Mr. Merton and his team propose an expected loss ratio and network measures, which scale and price the value of insurance and its change over time. A common measure of this guarantee cost is in the form of CDS spreads, but Merton uses the options market to come up with an estimate of what the spreads could have been if there were no government guarantees. This approach compares the output of the model with a time series of credit spreads as represented by one-year CDS for six countries and show that the model’s implied probability of default indicator tracks closely with actual market credit spreads. It facilitates a study to measure credit connectedness and influence amongst institutions with the help of Granger causality tests (please see below for details).

Contingent Claims Analysis & Merton’s Approach

Contingent claims analysis (CCA) is the application of option-pricing theory to the valuation of assets, which is pioneered by Black-Scholes (1973) and Merton (1973). CCA analyzes mismatches between an entity’s assets and liabilities. It is based on: 1) the values of liabilities are derived from assets; 2) liabilities have different priority; 3) assets follow stochastic claims.

The essence of CCA is that changes in observed variables are used to infer changes in unobserved variables. The application of CCA to capital structure derives from the seniority of liabilities and the balance sheet identity (D+E = A). Typically, the strategies include: 1) a direct change in financial structure; 2) managing guarantees; 3) risk transfer; 4) institutional changes to tailor the institutional structure to fulfill financial functions.

In Mr. Merton’s framework, “top-up guarantees” are considered along other items on the balance sheet when viewing sovereign debt, as the value of these guarantees tend to be enormous particularly in times of stress, when governments bail out banks and they write guarantees on the bank assets, which is similar to writing a put on a put at an accelerating rate. The point is that economy is a set of interrelated balance sheets with corporate sector (corporate asset, debt, equity), financial sector (loans, financial guarantees, debt/deposits/liabilities, equity), and public sector (foreign currency, net fiscal assts, financial guarantees, foreign currency debt, base money and local-currency debt). These three balance sheets are interdependent, and they can be analyzed like puts and calls (one sector long a certain implicit option and another sector short the same implicit option).

A financial guarantee is modeled as a put option, which is sensitive to the value of an underlying asset in a non-linear way and exhibits convexity. CCA models an issuer’s debt as a combination of risk-free debt and a short put option on the issuer’s assets. If the issuer default, the issuer has to give up the remaining value of the firm’s assets to the bondholder. The holder of the guarantee receives the promised value of the debt minus the value of assets recovered from the defaulting entity.  The Merton Model is an application of CCA for the valuation of corporate debt obligations. The values of the contingent claims on the CCA balance sheets contain embedded implicit options which can be used to obtain risk measures.

A Couple Words on Granger Causality Tests

The Granger causality test is a statistical hypothesis test for determining the validity of one time series in forecasting another. Specifically, Clive Granger’s methodology is that if a time series is stationary, the test is performed using the level values of two or more variables; if the variables are non-stationary, the test is done using first differences. Any particular lagged value of one of the variables is retained in the regression if 1) it is significant according to a t-test, and 2) it and the other lagged values of the variable jointly add explanatory power to the model according to an F-test. Then the null hypothesis of no Granger causality is retained if and only if no lagged values of an explanatory variable have been retained in the regression.

However, Granger causality test is not necessarily true causality – it may generate misleading results when the true relationship involves three or more variables and one might accept the alternative hypothesis of Granger causality.

Reference:

A New Framework for Analyzing and Managing Macrofinancial Risks of Economy – Dale F. Gray, Rober C. Merton, Zvi Bodie

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