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。

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.