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

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.

Option pricing and hedging for tempered stable jumps driven stochastic volatility models based on improved PSO algorithm

In order to capture leptokurtic feature, thick tail phenomenon in skewed financial returns, and capture heteroscedasticity effect, clustering effect in volatility diffusion process simultaneously, and to portray infinite jump changes in stock price dynamic process, the classical tempered stable (CTS) distribution in infinite activity pure jump Lévy distributions is introduced into the square root CIR process based stochastic volatility (SV) model to build an infinite activity tempered stable distribution driven stochastic volatility (CTSSV) model, thus we reconstruct the infinite activity Lévy process driven stochastic volatility (LVSV) model scheme. Using analytic characteristic function formula of LVSV model, and fractional fast Fourier transform (FRFT) technique, analytic European option pricing formula is derived. Because there are many numbers of model parameters and the difficulty of high dimensionality integration, we introduce multi-basin adaptive particle swarm optimization (MAPSO) algorithm to estimate LVSV model's parameters. Employ the characteristic function based FRFT technique and MAPSO parameter estimation techniques, we conduct experiment on Hang Seng Index Options data for option pricing and variance-optimal option hedging by CTS model and variance gamma stochastic volatility (VGSV) model. Empirical studies demonstrate the effectiveness and superiority of the MAPSO algorithm as well as the CTSSV model.