非仿射随机波动率模型下的50ETF期权定价基于Fourier-Cosine方法  

Fourier-Cosine based option pricing for SSE 50 ETF under non-affine stochastic volatility model

作　　者：孙有发[1] 吴碧云 郭婷 刘彩燕[2] SUN Youfa;WU Biyun;GUO Ting;LIU Caiyan(School of Economics and Commerce,Guangdong University of Technology,Guangzhou 510520,China;School of Management,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学经济与贸易学院,广州510520 [2]广东工业大学管理学院,广州510520

出　　处：《系统工程理论与实践》2020年第4期888-904,共17页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71771058);广东省自然科学基金(2017A030313400)。

摘　　要：非仿射随机波动率模型因其简约、且能较好刻画资产收益率分布的尖峰、厚尾、有偏等特性,近年来日益受到金融学界和业界的关注;然而,由非仿射随机波动率模型推导的衍生品定价方程,难以得到解析定价公式,因而其在实际应用中存在较大困难.应用扰动法处理标的资产对数价格的特征函数所满足的柯尔莫哥洛夫后向方程,得到特征函数的解析逼近式;然后应用FourierCosine方法,推导出欧式期权的拟闭型定价公式.上证50ETF期权定价的数值结果表明由推导的拟闭型定价公式计算得到的期权价格以及Greeks值,与市场价格和Wind资讯给出结果十分接近;且定价精度和效率明显优于当前同类型研究.本研究可望为上证ETF新期权品种提供一种高性能、应用级的定价和风险量化管理工具.The non-affine stochastic volatility model is attracting more and more attention from financial academic and industrial world in recent years,due to its parsimony and ability to characterize the excess kurtosis,fat tails as well as asymmetry exhibited in the distribution of asset return.However,at this moment the option market seldom witnesses its practical use,since under this model it is hard to obtain an analytic pricing formula for derivatives.To overcome this difficulty,a perturbation method is used in this paper to obtain an approximation of characteristic function of the logarithmic asset price by solving the associated Kolmogorov backward equation;then a Fourier-cosine-series method is applied to derive a quasi-closed formula for European option.Extensive numerical results from the Shanghai Stock Exchange(SSE) 50 Exchange Traded Fund(ETF) option pricing practices show that the calculated option prices and Greeks by our quasi-closed pricing formula are quite close to those from the real market and the Wind database,respectively;besides,our pricing formula outperforms those alternatives in current literature in both accuracy and efficiency.This research contributes to providing an alternative powerful tool of option pricing and quantitative risk management for SSE’s new ETF options.

关 键 词：期权定价 上证50ETF 随机波动率模型 非仿射 Fourier-Cosine方法 扰动法 

分 类 号：F830.9[经济管理—金融学]