Contingent Capital with a Capital-Ratio Trigger

34 Pages Posted: 1 Sep 2010

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Behzad Nouri

Columbia University

Date Written: August 31, 2010


Contingent capital in the form of debt that converts to equity when a bank faces financial distress has been proposed as a mechanism to enhance financial stability and avoid costly government rescues. Specific proposals vary in their choice of conversion trigger and conversion mechanism. We analyze the case of contingent capital with a capital-ratio trigger and partial and on-going conversion. The capital ratio we use is based on accounting or book values to approximate the regulatory ratios that determine capital requirements for banks. The conversion process is partial and on-going in the sense that each time a bank's capital ratio reaches the minimum threshold, just enough debt is converted to equity to meet the capital requirement, so long as the contingent capital has not been depleted. We derive closed-form expressions for the market value of such securities when the firm's assets are modeled as geometric Brownian motion, and these result in formulas for the fair yield spread on the convertible debt. A key step in the analysis is an explicit expression for the fraction of equity held by the original shareholders and the fraction held by converted investors in the contingent capital.

Suggested Citation

Glasserman, Paul and Nouri, Behzad, Contingent Capital with a Capital-Ratio Trigger (August 31, 2010). Available at SSRN: or

Paul Glasserman (Contact Author)

Columbia Business School ( email )

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Behzad Nouri

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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