Financial modelling and derivatives pricing under alternative Stochastic processes

替代随机过程下的金融建模和衍生品定价

• 批准号: 262275-2008
• 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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=548019
• 关键词: Financial; modelling; derivatives; pricing; under

The development of realistic stochastic models for risky asset price processes and their implementation to the pricing of generally exotic derivatives is at the heart of modern day financial mathematics. A vast body of research is devoted to this important area which poses computational and theoretical challenges. Current models go well beyond the celebrated Black-Scholes model which does not support commonly observed features such as volatility clustering and fat tail distributions for asset price returns. The observed leverage effect and the market implied volatility smiles are also completely absent in this model and not well replicated in some mathematical extensions of the model. The resolution of these model discrepancies is a fundamental issue and this continues to fuel interest in financial modelling and option pricing with the use of more realistic models. The goal of my research is to make further progress in this and related critical areas of financial mathematics. This proposal focuses on further innovative developments of alternative stochastic processes in the single and multi-asset domain with several applications to derivatives pricing. An underlying component of my research involves the use of our newly developed families of analytically tractable models. Our research to date has shown that our models are rich in their ability to realistically describe option market volatility smiles and skews. My most current work also develops analytically exact spectral expansions for first passage time densities, barrier options and seasoned lookback options for these new models. We have also recently succeeded in developing efficient algorithms for pricing exotic options under subfamilies of our new volatility smile models. This proposal will continue to build on new developments and applications of such alternative stochastic models. The development of efficient numerical algorithms for describing such processes leads to various applications in finance as well as in many other areas of mathematical modelling that involve stochastic processes. The mathematical and computational results that will be generated by this research are expected to significantly impact the field of financial mathematics.

危险资产价格过程的现实随机模型的开发及其对普遍异国情调衍生品的定价的实施是现代金融数学的核心。大量研究专门针对这一重要领域，构成了计算和理论挑战。当前的模型远远超出了著名的黑色 - 智能模型，该模型不支持通常观察到的功能，例如波动性聚类和资产价格回报的脂肪尾部分布。在该模型的某些数学扩展中，观察到的杠杆作用和市场隐含的波动性微笑也完全不存在。这些模型差异的解决是一个基本问题，这继续引起人们对财务建模和期权定价的兴趣，并使用更现实的模型。我的研究的目的是在金融数学的这一关键领域取得进一步的进步。该提案着重于单个和多资产域中替代随机过程的进一步创新发展，并具有多种用于衍生品定价的应用。我的研究的基本组成部分涉及使用新开发的分析模型家族。迄今为止，我们的研究表明，我们的模型具有现实描述期权市场波动性微笑和偏斜的能力。我目前的最新工作还为这些新型号的第一通道时间密度，障碍选项和经验丰富的回溯选项开发了分析上精确的光谱扩展。最近，我们还成功地开发了有效的算法，用于在我们新的波动性微笑模型的亚家族下定价异国选择。该建议将继续基于此类替代随机模型的新开发和应用。描述此类过程的有效数值算法的开发导致金融中的各种应用以及许多涉及随机过程的数学建模领域。这项研究将产生的数学和计算结果预计将显着影响金融数学领域。