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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=714140
• 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，金融数学是金融和数学的核心学科。随机过程为量化所有经济部门的金融风险提供了自然的环境。金融衍生品是在所有经济部门大量交易的或有债权。金融数学的一个重要领域仍然是开发和应用现实且易于处理的随机模型来描述风险因素以及这些模型在衍生品合约的估值和对冲中的实施。许多金融衍生品本质上也是路径依赖的。这种具有内在路径依赖性的复杂金融工具对于减轻特定风险很有用。此外，资产的某些类型的路径依赖性可以在将期权定价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，路径相关量（例如资产首次达到临界水平的时间或资产低于给定临界水平的占用时间）以及这些量的变化对于评估存在违约风险的金融合同非常有用。我的研究将集中于易于处理的随机模型的进一步新发展，并将模型应用于定量金融中的各种重要问题，包括风险建模、衍生品定价和对冲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和建立在我之前在所谓的可解模型上取得的进展以及当前和新的应用领域，这些领域也将期权定价和信用风险联系起来。该提案将为采用此类模型的金融应用带来新的模型和高效的数值算法。我研究的另一个部分将利用蒙特卡罗模拟算法。将使用不同的方法来开发易于处理的现实模型。一种方法将尝试将我们已经成功开发的单资产可解模型的数学方法扩展到多资产领域。另一种方法将利用联结函数构建易于处理的多资产模型，该模型将考虑一些实际市场观察到的影响。这些模型的实际实施将产生用于模型校准以及多资产金融产品定价和对冲的有效算法。一些算法还将利用高性能计算软件。