Stochastic Dynamic Programming and Monte Carlo Simulation for Valuing Corporate Debts

这个研究项目的目的是设计、求解和实现一组随机动态规划，用于1-评估公司债务，2-计算其收益率差，以及3-估计其违约概率。这些模型应该足够灵活，能够适应现实生活的复杂性，并且足够高效，能够与其他建筑相竞争。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显了信誉，因此有助于市场参与者避免财务困境和公司破产等不利事件，因为公司破产会导致公司债权持有人的价值损失和公司员工的职位损失。根据国际清算银行和证券业和金融市场协会的数据，2012年债券市场的未偿还总额约为100万亿美元，其中11%是由公司发行的。与美国公司债券市场不同，美国公司债券市场占全球公司债券市场的50%，而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。理论信号对缺乏流动性的市场最有帮助。对结构模型的贡献有一个主要的缺点。它们不够灵活，不足以容纳(全部)1-任意的公司债券投资组合，2-多个债券资历等级，3-偿债基金，4-嵌入债券的美国式期权，5-股息，6-税收优惠，7-破产成本，8-替代重组过程，9-州过程的各种马尔可夫动态，和/或10-多个信用风险实体。本研究项目试图将这些问题整合在一起。对于一维和二维模型，随机动态规划(SDP)将与有限元多项式近似相结合。这是准显式方法的极限。对于高维模型，SDP将与蒙特卡罗模拟和局部回归相结合。

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.