Pricing and Hedging under Processes with Conditional Independent Increments

有条件独立增量流程下的定价和对冲

• 批准号: RGPIN-2014-03664
• 负责人: Olivares, Pablo
• 金额: $ 0.8万
• 依托单位: Ryerson 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=661184
• 关键词: Pricing; Hedging; under; Processes; Conditional

Olivares, Pablo PIN: 346658**The general objective of the proposal is to develop techniques to price multidimensional derivative contracts and methods to obtain adaptive hedging strategies when the dynamic of the underlying assets is described by stochastic processes with conditional independent increments (PCII).*The proposal is divided in four interacting components with specific objectives: asset modelling, approximating pricing methods, adaptive hedging strategies and applications to energy and environmental finance.*Original contributions to scientific knowledge can be found in five main directions related with these components. Theoretical properties of new models, such as integrated characteristic functions, equivalent martingale measures, subordination, asymptotic behavior, mixed moments and first exit probability distributions will be investigated. Next, existing techniques for pricing will be adapted under the new circumstances. A combination of Fast Fourier methods, Taylor and other polynomial approximations, together with saddlepoint techniques will be taken into account. They are planned to be implemented to most common multidimensional derivatives, starting with European type contracts, and then considering Barriers and Defaultable Bonds, to Credit Derivatives Swaps (CDS), where default is given by PCII models. A novel method for hedging is proposed, where adaptive parameter estimation is studied from an optimal control perspective. Parameter estimation techniques based on approximated characteristic functions and a non parametric point of view will be developed at this stage. Finally, applications to the energy and the emerging environmental financial sectors will be explored, always under the new models in the class of PCIIs. It includes the pricing of real options with oil, heating oil and gasoline as underlying, as well as electricity prices.*The relevance of this research proposal lies in the novelty of the mathematics models considered as well as in the original implementation of approximated closed pricing formulas and adaptive hedging strategies derived from them. It may have a potential impact in financial institutions, specifically in the important Canadian energy sector, as it provides practitioners with more accurate tools and faster algorithm to evaluate investment positions based on multidimensional derivative products.*Results of the research will be incorporated to the existing programs in Financial Mathematics at Ryerson University, at undergraduate and graduate levels. It will be reflected in the development of our research group, the training of approximately 15 HQP, publication of 10 scientific papers in main stream journals as well as a general improvement in curricular activities.*The project viability is supported by author's past experience. The author has an ample base of collaborators at Ryerson University, University of Toronto, University of Montreal, Technical University of Munich, Florida International University, Autonomous Mexican Technological Institute among others. Students will be incorporated at all stages, with special emphasis in applications to energy and environmental finance.

Olivares, Pablo PIN: 346658** 该提案的总体目标是开发多维衍生品合约定价技术以及当标的资产的动态由具有条件独立增量 (PCII) 的随机过程描述时获得自适应对冲策略的方法。 *该提案分为四个具有特定目标的相互作用的组成部分：资产建模、近似定价方法、自适应对冲策略以及在能源和环境金融中的应用。*对科学知识的原创贡献可以在五个主要方面找到与这些组件相关的方向。将研究新模型的理论特性，例如积分特征函数、等效鞅测度、从属关系、渐近行为、混合矩和首次退出概率分布。接下来，现有的定价技术将在新形势下进行调整。将考虑快速傅里叶方法、泰勒和其他多项式近似以及鞍点技术的组合。它们计划应用于最常见的多维衍生品，从欧洲类型合约开始，然后考虑障碍和可违约债券，再到信用衍生品互换（CDS），其中违约由 PCII 模型给出。 提出了一种新的对冲方法，从最优控制的角度研究自适应参数估计。现阶段将开发基于近似特征函数和非参数观点的参数估计技术。最后，将始终在 PCII 类别的新模式下探索在能源和新兴环境金融领域的应用。它包括以石油、取暖油和汽油为基础的实物期权的定价，以及电价。*本研究提案的相关性在于所考虑的数学模型的新颖性以及近似封闭定价的原始实施公式和从中衍生的自适应对冲策略。它可能对金融机构产生潜在影响，特别是在重要的加拿大能源领域，因为它为从业者提供了更准确的工具和更快的算法来评估基于多维衍生产品的投资头寸。*研究结果将纳入现有的瑞尔森大学金融数学本科和研究生课程。这将体现在我们研究小组的发展、大约 15 名 HQP 的培训、在主流期刊上发表 10 篇科学论文以及课程活动的总体改进中。*项目的可行性得到了作者过去经验的支持。作者在瑞尔森大学、多伦多大学、蒙特利尔大学、慕尼黑工业大学、佛罗里达国际大学、墨西哥自治技术学院等机构拥有大量合作者。 学生将参与各个阶段的学习，特别注重能源和环境金融的应用。