基于改进PSO算法的调和稳定跳跃下随机波动模型期权定价与套期保值

发布时间：2018-01-18 15:10

本文关键词：基于改进PSO算法的调和稳定跳跃下随机波动模型期权定价与套期保值　出处：《系统工程理论与实践》2017年11期 　论文类型：期刊论文

【摘要】：为同时捕获金融收益率分布的尖峰、厚尾、有偏特性及波动率扩散中的异方差效应、集聚效应,联合刻画股价动态演变中的无限跳跃变化,将无限活跃纯跳跃Lévy分布中的经典调和稳定分布(CTS)引入平方根CIR模型为基础的随机波动率(SV)过程,建立了经典调和稳定分布下随机波动(CTSSV)模型,重构了纯跳跃Lévy分布驱动的随机波动(LVSV)模型框架.利用LVSV模型特征函数表达式,采用分数阶快速傅里叶变换(FRFT)方法推导了欧式期权定价公式.由于模型参数众多和目标函数高维积分困难,提出了多区域自适应粒子群优化算法(MAPSO)估计LVSV模型参数.利用FRFT技术和MAPSO参数估计结果,使用CTSSV模型和方差伽马随机波动(VGSV)模型对恒生指数期权数据进行欧式期权定价和方差一最优期权套期保值,实证研究结果证明了MAPSO算法的优越性和CTSSV模型的有效性.
[Abstract]:In order to capture the peak, thick tail, bias characteristic and heteroscedasticity effect of volatility diffusion, agglomeration effect is used to describe the infinite jump in the dynamic evolution of stock price. The classical harmonic stable distributions in infinite active pure jump L 茅 vy distributions are introduced into the stochastic volatility process based on the square root CIR model. The CTSSV model of stochastic wave under classical harmonic stable distribution is established. A pure jump L 茅 vy distribution-driven stochastic volatility VV (VV) model framework is reconstructed, and the eigenfunction expression of the LVSV model is used. The pricing formula of European option is derived by fractional fast Fourier transform (FRFT) method because of the numerous parameters of the model and the difficulty of high dimensional integration of the objective function. A multi-region adaptive particle swarm optimization (MPASO) algorithm is proposed to estimate the parameters of LVSV model, and the FRFT technique and the result of MAPSO parameter estimation are used. CTSSV model and variance gamma random volatility model are used to carry out European option pricing and variance optimal option hedging for Hang Seng Index option data. The result of empirical study proves the superiority of MAPSO algorithm and the validity of CTSSV model.
【作者单位】：东北大学工商管理学院;
【基金】：国家自然科学基金(71671030,71571038)~~
【分类号】：F224;F724.5
【正文快照】： i引言传统金融建模中资产价格动态过程服从几何布朗运动的假设不符合真实市场实际.金融资产收益过程通常表现出频繁的价格跳跃,收益率的波动过程具有集聚性和持续性,收益率分布呈现尖峰、厚尾及非对称'法等非高斯特性[1].在有限时间间隔内,资产价格跳跃由无数小跳跃与极端大

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