摘 要
随着金融市场全球化和金融工具复杂化，期权作为重要的衍生品在风险管理与资产配置中发挥着不可替代的作用，然而传统定价模型在应对非理想市场条件时存在局限性。本研究基于金融工程理论，结合现代数学方法与实证分析技术，旨在构建一种适应性强、精确度高的期权定价模型。通过引入跳跃-扩散过程改进Black-Scholes模型的假设框架，并利用蒙特卡洛模拟与有限差分法对模型进行数值求解，同时结合实际市场数据校准参数以提升模型的适用性。研究表明，改进后的模型能够有效捕捉标的资产价格的跳跃特性及波动率微笑现象，从而显著提高定价精度。此外，本研究还提出了一种基于机器学习算法的隐含波动率估计方法，进一步优化了模型的计算效率与稳健性。结果表明，该模型在处理非线性市场环境下的期权定价问题时表现出优越性能，为金融机构提供了更为可靠的决策支持工具。本研究的主要贡献在于突破了经典模型对市场连续性和正态分布的严格假设，同时将金融工程与计算科学深度融合，为未来相关领域的研究奠定了理论与实践基础。
关键词：期权定价 跳跃-扩散过程 蒙特卡洛模拟
Abstract
With the globalization of financial markets and the increasing complexity of financial instruments, options, as an essential derivative, play an irreplaceable role in risk management and asset allocation. However, traditional pricing models exhibit limitations when dealing with non-ideal market conditions. This study, grounded in financial engineering theory and integrating modern mathematical methods with empirical analysis techniques, aims to construct a robust and highly accurate option pricing model. By incorporating a jump-diffusion process to refine the assumption fr amework of the Black-Scholes model, this research employs Monte Carlo simulation and finite difference methods for numerical solutions while calibrating parameters using real market data to enhance model applicability. The findings indicate that the improved model effectively captures the jump characteristics of underlying asset prices and the volatility smile phenomenon, thereby significantly enhancing pricing accuracy. Furthermore, this study proposes a machine learning-based algorithm for estimating implied volatility, which further optimizes computational efficiency and model robustness. Results demonstrate superior performance of the model in addressing option pricing problems under nonlinear market environments, providing financial institutions with a more reliable decision-support tool. The primary contribution of this study lies in breaking through the strict assumptions of classical models regarding market continuity and normal distribution, while deeply integrating financial engineering with computational science, thus laying a theoretical and practical foundation for future research in related fields.
Keyword:Option Pricing Jump-Diffusion Process Monte Carlo Simulation
目 录
1绪论 1
1.1期权定价模型的研究背景与意义 1
1.2国内外研究现状分析 1
1.3研究方法与技术路线 1
2金融工程基础理论与期权定价框架 2
2.1金融工程的核心概念与工具 2
2.2期权定价的基本原理 2
2.3常见期权定价模型的比较分析 3
2.4模型选择与适用性探讨 3
3期权定价模型的构建与优化 4
3.1黑 4
3.2跳跃扩散模型的应用研究 4
3.3随机波动率模型的改进分析 5
3.4复杂衍生品定价的技术挑战 5
4实证分析与案例研究 6
4.1数据来源与样本选择 6
4.2模型参数估计与校准 6
4.3实证结果分析与讨论 7
4.4模型应用中的问题与对策 7
结论 7
参考文献 9
致谢 10
