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In this paper we provide concrete evaluations for the trigger price that causes the conversion of Convertible Contingent (CoCo) bond contracts.In particular we exploit prices for CoCo bonds traded in real financial markets and the values obtained by the credit derivative as well as by the equity derivative method, to determine the associated implicit trigger price. Because of the computational characteristics of the proposed approaches, we also provide related algorithms.

In the present paper we consider the Default Risk Charge (DRC) measure as an effective alternative to the Incremental Risk Charge (IRC) one, proposing its implementation by a quasi exhaustive-heuristic algorithm to determine the minimum capital requested to a bank facing the market risk associated to portfolios based on assets issued by several financial agents. While most of the banks use the Monte Carlo simulation approach and the empirical quantile to estimate this risk measure, we provide new computational approaches, exhaustive or heuristic, currently becoming feasible because of both the new regulation and to the high speed - low cost technology available nowadays. Concrete algorithms and numerical examples are provided to illustrate the effectiveness of the proposed techniques.

Our study investigates the optimal dividend strategy for a bank, taking into account the potential for government capital injections. We explore different types of government interventions, such as liberal, transparent, or uncertain strategies, and consider both single and multiple types of interventions. Our approach differs from others as it focuses on interventions that aim to maintain the overall stability of the financial system, rather than just addressing banks that have already sought government assistance or are in dire need of it. Specifically, we focus on situations where the government is more likely to assist banks that have not requested its intervention or that are not too difficult to save. To accomplish this, we conduct a comprehensive examination of all possible scenarios involving a single, one-time capital injection and derive explicit solutions for the associated optimal control problem. Furthermore, we expand the model to include semi-Markov dynamic capital injection processes and show that the optimal control is the unique viscosity solution of a Hamilton–Jacobi–Bellman equation. The government’s strategy also takes into account the bank’s solvency and any past government interventions.