Callable risky perpetual debt with protection period

Abstract

Abstract. Issuances in the USD 260 Bn global market of perpetual risky debt are often motivated by capital requirements for financial institutions. We analyze callable risky perpetual debt emphasizing an initial protection ('grace') period before the debt may be called. The total market value of debt including the call option is expressed as a portfolio of perpetual debt and barrier options with a time dependent barrier. We also analyze how an issuer's optimal bankruptcy decision is affected by the existence of the call option by using closed-form approximations. The model quantifies the increased coupon and the decreased initial bankruptcy level caused by the embedded option. Examples indicate that our closed form model produces reasonably precise coupon rates compared to numerical solutions. The credit-spread produced by our model is in a realistic order of magnitude compared to market data.

Level-Dependent Annuities: Defaults of Multiple Degrees

“…Preferred stock, issued by banks and insurance companies as part of their risk capital, is another example of possible applications. The issuer of such claims is entitled to drop coupon payments in financial distress, potentially conditional upon no dividend payments on common stock (see, e.g., Emanuel (1983), Mjøs and Persson (2010)). Novel structured financial products and special purpose vehicles are other likely areas of application.…”