Collaborative Research: Market-Based Calibration of Pricing Models for Financial and Energy Option Contracts

这项拟议的研究要求为开发高性能计算工具提供资金，以便利用现有的市场数据快速准确地校准金融和能源期权合同的定价模型。这项研究的结果将被用来确定各种期权定价模型的参数，这些模型放宽了广泛使用的Black-Scholes-Merton模型的限制性假设。对于欧式期权，我们研究了求解离散偏积分-微分方程组约束的最优化问题的算法。对于具有早期解题特征的美式期权，我们发展了具有互补约束的数学规划的有效求解技术。我们还研究了求解美式期权定价的抛物型变分不等式半离散化所产生的线性互补系统的各种方法。如果成功，拟议的研究结果将导致对金融和能源期权定价模型的准确校准，这是一个对许多行业组成部分具有根本性重要性的实际问题，包括金融公司、养老金和共同基金经理、市场参与者、能源生产商和商品生产商，他们将期权合约用作对冲工具，以防范利率、货币汇率、股票价格、能源和大宗商品价格的大幅价格波动。改进的定价模型以更适当的方式对与基础金融变量相关的风险进行建模，将产生更好的投资决策，并将有助于减少套利机会和稳定金融市场。我们的研究结果也将有益于数学规划领域和其他服务行业，在这些行业中，类似的模型校准问题非常重要。

This proposed research requests funding for the development of high performance computational tools for the fast and accurate calibration of pricing models for financial and energy option contracts using available market data. The results of this research will be used to determine the parameters of various option pricing models that relax the restrictive assumptions of the widely used Black-Scholes-Merton model. For options of the European type, we investigate algorithms for solving optimization problem constrained by discretized partial integro-differential equations. For options of the American type with early exercise features, we develop efficient solution techniques for mathematical programs with complementarity constraints. We also investigate various methods for solving linear complementarity systems arising from the semi-discretization of parabolic variational inequalities for the valuation of American type options. If successful, the results of the proposed research will lead to the accurate calibration of financial and energy option pricing models, a practical problem that is of fundamental importance to many industrial constituents, including financial firms, pension and mutual fund managers, market participants, energy generators, and commodity producers, who use option contracts as hedging tools to safeguard against large price fluctuations in interest rates, currency exchange rates, equity prices, energy and commodity prices. Improved pricing models in which risks associated with the underlying financial variables are modeled in more appropriate ways will yield better investment decisions and will help reduce arbitrage opportunities and stabilize the financial markets. The results of our research will also benefit the mathematical programming field and other service industries where similar model calibration problems are important.