Stochastic Dynamic Programming and Monte Carlo Simulation for Valuing Corporate Debts

本研究计划的目的是设计、解决并实施一套随机动态计划，用于1-评估公司的公司债务，2-计算其收益率差，3-估计其违约概率。这些模型应该足够灵活，以适应现实生活的复杂性，并且足够有效，与其他结构竞争。金融证券的公允价值构成了交易的指南，因此增加了资本市场的效率。上市公司的收益率差和违约概率突出了信誉，因此，帮助市场参与者避免财务困境和不利事件，如公司破产，这会给公司的索赔人带来价值损失，给公司的工人带来职位损失。根据国际清算银行和证券业与金融市场协会的数据，2012年债券市场的未偿总额约为100万亿美元，其中11%由公司发行。与占全球公司债券市场50%的美国公司债券市场不同，加拿大公司债券市场规模较小，多元化程度较低，因此效率较低。理论信号对流动性不足的市场最有帮助。

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.