Solvable and Other Stochastic Models for Risk Modeling and Asset Pricing in Quantitative Finance

定量金融中风险建模和资产定价的可解模型和其他随机模型

• 批准号: RGPIN-2018-06176
• 负责人: Campolieti, Giuseppe
• 金额: $ 1.17万
• 依托单位: Wilfrid Laurier University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=646775
• 关键词: Solvable; Other; Stochastic; Models; Risk

Stochastic modelling is fundamental to financial mathematics, which is a core discipline in both finance and mathematics. Stochastic processes provide a natural setting for quantifying financial risk in all sectors of the economy. Financial derivatives are contingent claims that are heavily traded in all sectors of the economy. An important area of financial mathematics remains the development and application of realistic and tractable stochastic models for describing risk factors and the implementation of these models in the valuation and hedging of derivative contracts. Many financial derivatives are also inherently path-dependent. Such complex financial instruments, with built-in path dependencies, are useful for mitigating specific risks. Moreover, certain types of path dependencies of an asset can play a key role in linking option pricing with the credit risk associated to a given financial firm. For example, path-dependent quantities such as the first passage time of an asset to a critical level or the occupation time of the asset below a given critical level, as well as variations of such quantities, are useful for valuing financial contracts subject to default risk. My research will focus on further new developments of tractable stochastic models and implementing the models to various important problems in quantitative finance involving risk modelling, derivative pricing and hedging, and model calibration to historical market data. A main part of my research will continue to exploit and build upon my previous advancements on so-called solvable models with current and new areas of application that will also link option pricing and credit risk. This proposal will lead to new models and efficient numerical algorithms for financial applications employing such models. Another component of my research will exploit Monte Carlo simulation algorithms. Different approaches will be used to develop tractable realistic models. One approach will attempt to extend the mathematical methodology that we have already successfully developed for single-asset solvable models into the multi-asset domain. The other methodology will exploit the use of copulas in constructing tractable multi-asset models that will take into account some real market observed effects. The actual implementation of these models will lead to efficient algorithms for model calibration and pricing and hedging multi-asset financial products. Some of the algorithms will also exploit the use of high-performance computing software.

随机建模是金融数学的基础，这是金融和数学的核心学科。随机过程为量化经济各个部门的财务风险提供了自然环境。金融衍生品是一定的主张，在经济的所有领域都进行了大量交易。金融数学的一个重要领域仍然是现实且可进行的随机模型的开发和应用，以描述风险因素以及在衍生合同的估值和对冲中实施这些模型。许多金融衍生品也固有地依赖路径依赖性。具有内置路径依赖性的这种复杂金融工具可用于缓解特定风险。此外，资产的某些类型的路径依赖性可以在将期权定价与与给定金融公司相关的信用风险联系起来方面发挥关键作用。例如，与路径依赖的数量（例如资产的第一个通过时间到临界水平的第一个通过时间或资产的职业时间低于给定的临界水平，以及此类数量的变化，对于评估符合违约风险的财务合同的评估很有用。我的研究将集中在可拖动随机模型的进一步发展上，并将模型实施到涉及风险建模，衍生定价和对冲的定量融资中的各种重要问题，以及对历史市场数据的模型校准。我的研究的主要部分将继续利用我以前在具有当前和新应用领域的可解决模型上的进步，这也将链接期权定价和信用风险。该建议将为使用此类模型的财务应用程序提供新的模型和有效的数值算法。我的研究的另一个组成部分将利用蒙特卡洛模拟算法。不同的方法将用于开发可聊天的现实模型。一种方法将尝试扩展我们已经成功开发的单位可解决模型的数学方法论到多资产域。另一种方法将利用Copulas在构建可拖动的多资产模型中的使用，这些模型将考虑到一些实际的市场观察到的效果。这些模型的实际实施将导致用于模型校准和定价和对冲多资产金融产品的有效算法。某些算法还将利用高性能计算软件的使用。