Dynamic models for credit spreads and credit correlations

信用利差和信用相关性的动态模型

• 批准号: 92966-2007
• 负责人: Hurd, Thomas
• 金额: $ 1.17万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=390794
• 关键词: Dynamic; models; credit; spreads; correlations

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.

复杂的数学模型现已被纳入《巴塞尔 II 资本计量和资本标准协议》，作为全球金融业监管环境中至关重要的战略要素。也许该领域最令人兴奋的开放研究课题是信用风险问题，其基本形式是对公司债券市场的动态（特别是违约原因）以及目前已知的股票和固定收益市场的动态进行建模。从数学上讲，这意味着开发一个无套利（NA）框架，其中嵌套了股票、政府债券和上市公司违约风险债券的定价，这意味着对所有相关衍生证券（包括信用违约掉期和债务抵押债券（CDO）等重要产品）的定价和对冲采用一致的方法。准确的信贷框架将带来更可靠的金融交易和风险管理系统，有助于稳定世界市场，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。我的建议是开发赫德和库兹涅佐夫于 2005 年提出的多企业仿射马尔可夫链 (AMC) 框架的有用且准确的实现，并将 AMC 建立为领先的信用风险数学框架。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；开发校准技术以使这些公式适合市场数据。在此过程中开发的技术，例如 CDO 的鞍点方法和随机时间变化方法，也将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，我的建议还将对 HQP 产生额外的影响：我的研究助理在离开 PhiMAC（麦克马斯特大学金融数学实验室）后，将在加拿大和全世界的金融行业和学术界对关键职业有很高的需求。