Dynamic models for credit spreads and credit correlations

复杂的数学模型现已载入《巴塞尔协议II》《资本衡量和资本标准》，认为这是全球金融业监管环境中极为重要的战略要素。或许这一领域最令人兴奋的公开研究主题是信用风险问题，其基本形式是对公司债券市场的动态进行建模，特别是违约的原因，并结合现在已知的股票和固定收益市场的动态。从数学上讲，这意味着开发一个无套利(NA)框架，该框架嵌套了股票、政府债券和上市公司违约风险债券的定价，然后意味着对所有相关衍生证券的定价和对冲的一致方法，包括信用违约互换(CDO)和债务抵押债券(CDO)等重要产品。准确的信贷框架将带来更可靠的金融交易和风险管理体系，有助于稳定全球市场，使其免受未来不可避免的违约冲击，如安然、世通等公司的违约冲击。我的建议是对赫德和库兹涅佐夫在2005年提出的多公司仿射马尔可夫链(AMC)框架进行有用和准确的实现，并将AMC建立为信用风险的领先数学框架。要实现一个有用的AMC模型，需要完成三项任务：将其组成部分与违约强度的市场驱动因素联系起来；推导市场交易信用产品的定价公式；开发校准技术，使这些公式符合市场数据。沿途发展起来的技术，例如CDO的鞍点法和随机时间变化法，也将被应用于扩展现有的信贷方法。除了对银行、投资基金和保险公司的交易和风险管理的潜在影响外，我的提议还将对HQP产生额外的影响：我的研究助理离开PhiMAC(麦克马斯特金融数学实验室)后，无论是在加拿大还是在世界各地，金融行业和学术界的关键职业都将受到高度需求。

Sophisticated mathematical modelling has now been enshrined in the Basel II Accord on Capital Measurement and Capital Standards as a strategic element of paramount importance in the regulatory environment of the global finance industry. Perhaps the most exciting open research topic in this area is the credit risk problem, a basic form of which is to model the dynamics of the corporate bond market, in particular the causes of defaults, jointly with the now understood dynamics of stock and fixed income markets. Mathematically, it means to develop a no-arbitrage (NA) framework which nests the pricing of equities, government bonds, and the default risky bonds of publicly listed corporations, which then implies a consistent methodology for pricing and hedging all associated derivative securities, including important products such as credit default swaps and collateralized debt obligations (CDOs). An accurate credit framework would lead to more reliable financial trading and risk management systems, helping to stabilize the world's markets from inevitable future default shocks as dramatic as those of Enron, WorldCom and the like. My proposal is to develop useful and accurate realizations of the multifirm Affine Markov Chain (AMC) framework introduced in 2005 by Hurd and Kuznetsov, and to establish AMC as a leading mathematical framework for credit risk. Realization of a useful AMC model requires completion of three tasks: to connect its components with the market drivers of default intensity; to derive pricing formulas for market traded credit products; to develop calibration techniques to fit these formulas to market data. Techniques developed along the way, for instance the saddlepoint method for CDOs, and the method of stochastic time change, will also be applied to extend existing credit methods. Beyond its potential impact on trading and risk management for banks, investment funds and insurance companies, my proposal will have an additional impact on HQP: my research associates, as they leave PhiMAC (the Financial Mathematics Lab at McMaster), will be in high demand for key careers both in the finance industry and academia, both in Canada and worldwide.