基于随机波动率状态转移特征的上证50ETF期权定价  

Pricing of SSE 50ETF Options Based on Stochastic Volatility Models with Regime Switching Features

作　　者：李坤昊 秦学志[1] LI Kunhao;QIN Xuezhi(School of Economics and Management,Dalian University of Technology,Dalian 116024,China;School of Economics,Fudan University,Shanghai 200433,China)

机构地区：[1]大连理工大学经济管理学院,辽宁大连116024 [2]复旦大学经济学院,上海200433

出　　处：《运筹与管理》2023年第7期162-169,共8页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(71871040,71471026);国家自然科学基金重点项目(71731003);国家社科基金重大项目(18ZDA095);辽宁省“兴辽英才计划”哲学社会科学领军人才项目(XLYC1804005)。

摘　　要：期权定价模型的构建过程中,单因子随机波动率模型生成的波动率曲线形状与波动率水平相关性微弱,且无法确切反映波动过程的状态转移特征。为此,本文使用连续马尔可夫链刻画波动状态,在Heston模型的基础上,针对其方差动态过程中所有参数均为波动状态任意函数的情景,得到了一类具有状态转移特征的随机波动率模型;进一步,根据条件仿射模型的特征函数,结合波动路径的蒙特卡罗模拟,实现了欧式期权半解析定价,其中,采用基于粒子滤波的极大似然估计方法估计模型参数;特别地,对上证50ETF期权进行了实证研究。结果表明:具有状态转移特征且方差的基准长期均值及波动率均依赖于波动状态的随机波动率模型,能够显著提升上证50ETF期权定价的准确性和稳健性。Accurate pricing is one of the prerequisites to ensure options functioning well in financial markets.Stochastic volatility models are widely used in option pricing as they can generate volatility smiles as well as term structures.However,the shape of volatility curves generated by one-factor stochastic volatility models has weak correlation with real fluctuating level,and cannot accurately reflect the regime switching characteristics of the volatility process as well.Adding state variables which describe regime switching characteristics of the volatility processes to stochastic volatility models can hopefully better describe the shapes of volatility surfaces as well as their dynamic processes,thus improving pricing accuracy.The application of stochastic volatility models with regime switching features in European option pricing has received growing attention for the past few years.However,in terms of model construction,existing research typically limits the relationship between volatility processes and the switching regime,without involving the adaptation of models to market features,and also without further discussion of their performance in certain option markets.In terms of pricing methods,when only the long-term mean is assumed to rely on a switching regime,a closed solution for European option pricing can be obtained.However,for other stochastic volatility models with regime switching features,closed solutions for option pricing are difficult to obtain.Existing research generally uses perturbation analysis or numerical methods to obtain option prices,failing to achieve balance between pricing accuracy and computational efficiency.In terms of the pricing of SSE 50ETF options,models and methods in existing research contribute to the improvement of SSE 50ETF option pricing accuracy,but have not taken regime switching features of volatility into account.However,according to iVIX data,the volatility of SSE 50ETF has regime switching features.Therefore,we aim to construct a stochastic volatility model with regime

关 键 词：期权定价 状态转移 随机波动率 上证50ETF期权 粒子滤波 

分 类 号：F830[经济管理—金融学]