Stochastic Modelling in Finance

金融中的随机建模

• 批准号: 341858-2013
• 负责人: Makarov, Roman
• 金额: $ 0.8万
• 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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=572386
• 关键词: Stochastic; Modelling; Finance

News coming from financial markets has a profound impact on people's everyday lives. Rising interest rates lead to larger mortgage payments. Fluctuations of crude oil prices are propagated into gas price tags. The credit rating of a government affects the yield rate of bonds issued to cover the budget deficit. The importance and complexity of financial markets explain the rapid development of financial mathematics in the last three decades. Mathematical modelling is a main research approach to describing and studying complex real-world systems such as financial markets where millions of transactions are made every day. Stochastic processes are a perfect instrument for the simulation of such dynamically changing uncertain systems with many coupled degrees of freedom. That is why stochastic modelling is at the core of financial mathematics. The focus of this research is the development and implementation of methods to help quantify and control financial risk. Modern day financial markets offer and trade increasingly more complex products. A path-dependent derivative is a financial contract whose value depends on the time history of values of other, more basic, underlying financial variables. Such options have become increasingly popular over the last few years because of the greater precision with which they allow investors to choose or avoid exposure to well-defined sources of risk. The numerical part of the proposed project is devoted to high-performance computational methods for pricing and hedging path-dependent financial instruments. To take into account realistic market effects such as price jumps, stochastic volatility, liquidity issues, and credit risk, many sophisticated financial models have been proposed. However, models used by practitioners for controlling risk are often too simplistic. By developing more realistic but still tractable stochastic models along with pricing and hedging algorithms and software, we can facilitate the implementation of recent achievements of financial mathematics in industry. Such models provide a flexible framework to account for many real market effects. On the other hand, we are able to construct closed-form solutions or efficient numerical algorithms for pricing various financial instruments.

来自金融市场的新闻对人们的日常生活产生了深远的影响。利率上升导致更大的抵押贷款。原油价格的波动传播到汽油价格标签中。政府的信用评级会影响为支付预算赤字的发行债券的收益率。金融市场的重要性和复杂性解释了过去三十年中金融数学的快速发展。数学建模是描述和研究复杂现实世界系统（例如金融市场）的主要研究方法，每天进行数百万笔交易。随机过程是模拟具有许多耦合自由度的动态不确定系统的理想工具。这就是为什么随机建模是金融数学的核心。这项研究的重点是开发和实施有助于量化和控制财务风险的方法。现代金融市场提供和贸易越来越复杂。依赖路径的衍生产品是一项财务合同，其价值取决于其他，更基本的，基本的财务变量的价值的时间历史。在过去的几年中，这种选择变得越来越流行，因为他们允许投资者选择或避免暴露于定义明确的风险来源的精确度。拟议项目的数值部分致力于用于定价和对冲路径依赖金融工具的高性能计算方法。为了考虑到现实的市场影响，例如价格上涨，随机波动性，流动性问题和信用风险，已经提出了许多复杂的财务模型。但是，从业者使用用于控制风险的模型通常过于简单。通过开发更现实但仍然可以处理的随机模型，以及定价和对冲算法和软件，我们可以促进在行业中金融数学的最新成就的实施。这样的模型提供了一个灵活的框架，以说明许多实际的市场影响。另一方面，我们能够构建封闭形式的解决方案或有效的数值算法来定价各种金融工具。