Grant: Discovery Grants Program - Individual

The aim of this research project is to design, solve, and implement a set of stochastic dynamic programs for 1- valuing a firm's corporate debt, 2- computing its yield spread, and 3- estimating its default probability. These models should be flexible enough to accommodate real-life complexities, and efficient enough to compete favourably with alternative constructions. Fair values of financial securities constitute a guide for trading, and, therefore, add efficiency to capital markets. The yield spreads and default probabilities of public companies highlight creditworthiness, and, therefore, help market participants avoid financial distress and adverse events such as corporate bankruptcy, which generates a loss of value for the firm's claimholders and a loss of positions for the firm's workers. According to the Bank for International Settlements and the Securities Industry and Financial Markets Association, the total outstanding amount in the bond market is around US$100 trillion in 2012, among which 11% are issued by corporations. Unlike the US corporate bond market, which represents 50% of the worldwide corporate bond market, the Canadian one is smaller and less diversified, and, thus, less efficient. Theoretical signals are the most helpful for illiquid markets.The contributions to the structural model suffer from one major downside. They are not flexible enough to accommodate (all together) 1- arbitrary corporate-bond portfolios, 2- multiple bond seniority classes, 3- sinking funds, 4- American-style options embedded in bonds, 5- dividends, 6- tax benefits, 7- bankruptcy costs, 8- alternative reorganization processes, 9- various Markov dynamics for the state process, and/or 10- multiple credit-risk entities. This research project attempts to integrate these issues, all together. For one- and two-dimensional models, stochastic dynamic programming (SDP) will be coupled with finite-elements polynomial approximations. This is at the limit of the quasi-explicit approach. For higher dimensional models, SDP will be coupled with Monte Carlo simulation and local regressions.