Financial Risk Modelling and Analysis

数学和统计建模用于描述和分析自然界和人类社会中出现的复杂现象。随机过程是对具有不确定性和多自由度的动态变化系统进行建模的理想工具。这种复杂系统的例子是每天有数百万笔交易的金融市场。更准确和更彻底地掌握市场价格行为的能力对加拿大各大银行和养老基金等各种金融机构非常重要。发展有效的数学金融数值和统计方法以及可解随机波动率模型的计算实现是拟议研究计划的主要优先事项。它有以下三个目标。首先，我们将开发一系列具有系统性风险的多资产定价模型，并评估它们在投资组合管理、衍生品定价和风险评估中的应用。拟议的模型允许处理具有缺失和不同步定价数据的金融资产。可以轻松地将新资产包括在模型中，而无需重新校准其他资产的参数。其次，我们将建立基于占用时间的信用风险结构模型。在这些模型中，违约时间被定义为企业的价值过程在违约障碍之下的占用时间首次超过给定的阈值。这种结构模型可用于评估清算风险，并允许将违约和清算事件分开。我们主要关注占用时间模型的校准，以及它们在信用违约互换和或有资本债券等金融风险工具定价中的应用。此外，我们还将评估频谱展开在对占用时间衍生品定价方面的应用。第三，开发金融新闻分析统计模型，并与资产价格模型相结合。一个目标是揭示金融新闻和其他公告如何影响股市，无论是股票价格的变化还是日成交量的变化。此外，我们还将把文本财经新闻算法的分类与资产价格模型结合起来，建立一个新闻驱动的股票市场模型。这项研究计划的结果将帮助我们更好地理解如何在数据不完整时对金融市场进行建模和评估风险，以及如何从非结构化的商业数据中提取有用的信息。

Mathematical and statistical modelling is used to describe and analyze complex phenomena arising in nature and human societies. Stochastic processes are a perfect instrument for modelling dynamically changing systems with uncertainty and multiple degrees of freedom. Examples of such complex systems are financial markets with millions of transactions made every day. The ability to capture the behaviour of market prices more accurately and more thoroughly is of significant importance to various financial institutions such as major Canadian banks and pension funds. The development of efficient numerical and statistical methods of mathematical finance and computational implementation of solvable stochastic volatility models are the main priorities of the proposed research program. It has the following three objectives. First, we will develop a family of multi-asset pricing models with a systemic risk component and evaluate their applications in portfolio management, derivative pricing and risk assessment. The proposed models allow for dealing with financial assets that have missing and asynchronous pricing data. New assets can be easily included in the model without recalibrating parameters for other assets. Second, we will develop structural models of credit risk based on occupation time. In these models, the time of default is defined as the first time that the occupation time of the firm's value process below a default barrier has exceeded a given threshold. Such structural models can be used to assess the liquidation risk and allow for separating default and liquidation events. Our primary focus is on the calibration of occupation time models, their applications in the pricing of financial risk instruments such as credit default swaps and contingent capital bonds. Additionally, we will evaluate the application of spectral expansions for pricing occupation time derivatives. Third, we will develop statistical models for financial news analysis and integrate them with asset price models. One objective is to uncover how financial news and other announcements can affect the stock market, whether that be changes in the price of a stock or changes in the daily volume. Additionally, we will develop a news-driven model of the stock market by combining the classification of textual financial news algorithm with asset price models. The results of this research program will help us better understand how to model financial markets and assess risks when data are incomplete, as well as how to extract useful information from unstructured business data.