Option Pricing with Multivariate GARCH Models

多元 GARCH 模型的期权定价

• 批准号: RGPIN-2020-05041
• 负责人: Stentoft, Lars
• 金额: $ 1.97万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740368
• 关键词: Option; Pricing; Multivariate; GARCH; Models

The ultimate goal of this research program is to 1) develop a multivariate statistical modelling framework, flexible enough to describe the dynamics and to take into account the correlations among financial assets, which can be used for risk management, in general, and option pricing, in particular, in high dimensions, and 2) provide the tools that regulators and supervisors crucially need to increase financial stability and that practitioners in financial institutions need to rapidly evaluate their risk exposures, improving market liquidity, and allow the financial markets to price and bear risk more efficiently. With the proposed model, derivatives on multiple assets can be priced in a theoretically consistent way and the research program develops innovative closed form readily computed expressions or formulas for derivatives pricing in this framework. Currently, the only possible methods for option pricing in such a flexible framework rely on time consuming numerical techniques like Monte Carlo simulation, and pricing securities in a timely manner requires shortcuts which sacrifice realism in the models. Closed form formulas, on the other hand, allow for fast and accurate pricing of the complex derivatives that exist in today's financial markets. The proposed framework also allows derivation of closed form expression for option price sensitivities. These measures are used to assess the risks of these derivative products and necessary for efficient management of the risks associated with such assets. Financial institutions and government regulators frequently perform such calculations to manage the risk of portfolios with thousands of assets. Therefore, closed form solutions are of immense importance because they allow reliable risk management in real time without sacrificing precision. The formulas derived in this research make it possible to incorporate historical option prices in the model estimation, leading to more efficient estimates of model parameters. Incorporating historical option prices in this multivariate framework also allows for calculating innovative measures of the perceived risk in financial markets that take into consideration the complex nature and interdependence of these markets. These innovative measures will lead to better and more consistent assessment of the risks involved in complex products than what is currently available. The flexible framework developed in this project will be of interest to academics, financial industry practitioners, and regulators. The proposed models have implications for how financial derivatives are valued, how their risks are managed, and therefore on how financial policy should be created, implemented, and evaluated. The proposed research program will greatly benefit the Canadian economy by providing tools to improve market liquidity and allow financial markets to efficiently price and bear risk, increasing financial stability and decreasing the likelihood of future financial crises.

该研究计划的最终目标是 1) 开发一个多元统计建模框架，该框架足够灵活，可以描述动态并考虑金融资产之间的相关性，一般可用于风险管理和期权定价，特别是在高维度上，2）为监管者和监督者提供提高金融稳定性所迫切需要的工具，以及金融机构从业者快速评估其风险敞口、提高市场流动性并允许金融市场定价和承担的工具。更有效地承担风险。通过所提出的模型，多种资产的衍生品可以以理论上一致的方式定价，并且该研究项目在此框架中开发了创新的封闭式易于计算的表达式或衍生品定价公式。目前，在这种灵活的框架中唯一可能的期权定价方法依赖于蒙特卡罗模拟等耗时的数值技术，而及时定价证券需要捷径，而这会牺牲模型的真实性。另一方面，封闭式公式可以对当今金融市场中存在的复杂衍生品进行快速、准确的定价。 所提出的框架还允许导出期权价格敏感性的封闭式表达式。这些措施用于评估这些衍生产品的风险，并且是有效管理与此类资产相关的风险所必需的。金融机构和政府监管机构经常进行此类计算，以管理拥有数千种资产的投资组合的风险。因此，封闭式解决方案非常重要，因为它们可以在不牺牲精度的情况下实现可靠​​的实时风险管理。 本研究得出的公式使得将历史期权价格纳入模型估计成为可能，从而更有效地估计模型参数。将历史期权价格纳入这个多元框架还可以计算金融市场感知风险的创新指标，同时考虑到这些市场的复杂性和相互依赖性。这些创新措施将比目前可用的措施更好、更一致地评估复杂产品所涉及的风险。 该项目开发的灵活框架将引起学术界、金融行业从业者和监管机构的兴趣。所提出的模型对于如何评估金融衍生品、如何管理其风险以及如何制定、实施和评估金融政策具有影响。拟议的研究计划将通过提供改善市场流动性的工具，使金融市场能够有效地定价和承担风险，从而提高金融稳定性并降低未来发生金融危机的可能性，从而极大地造福加拿大经济。