Dynamic models for credit spreads and credit correlations

复杂的数学模型现已被载入《关于资本计量和资本标准的巴塞尔II雅阁》，作为全球金融业监管环境中至关重要的战略要素。在这一领域，最令人兴奋的开放式研究课题可能是信用风险问题，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，以及现在所了解的股票和固定收益市场的动态。在数学上，它意味着开发一个无套利（NA）框架，该框架嵌套股票，政府债券和上市公司的违约风险债券的定价，这意味着一种一致的方法来定价和对冲所有相关的衍生证券，包括信用违约掉期和债务抵押债券（CDO）等重要产品。一个准确的信贷框架将导致更可靠的金融交易和风险管理系统，有助于稳定世界市场，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。我的建议是开发有用的和准确的实现的多公司仿射马尔可夫链（AMC）框架在2005年由赫德和库兹涅佐夫，并建立AMC作为信用风险的领先数学框架。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;推导出市场交易信贷产品的定价公式;开发校准技术，使这些公式与市场数据相匹配。沿着这条道路发展起来的技术，例如CDO的鞍点方法和随机时间变化方法，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产生潜在影响外，我的提议还将对HQP产生额外影响：我的研究伙伴离开PhiMAC（麦克马斯特金融数学实验室）后，将在加拿大和全球金融行业和学术界的关键职业中受到高度需求。

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.