波动率建模新视角: 无套利局部波动率曲面--以上证50ETF期权市场为例

Based on a New Perspective on Volatility Modeling of Arbitrage-free Local Volatility Surfaces:Take SEE 50ETF Op-tions as an Example

基于SVI函数、平远期插值和Dupire公式,提出NALVS局部波动率建模算法,成功解决了中国期权市场上“有套利”和“少数据”两大难题,构建得到上证50ETF期权无套利局部波动率曲面。研究发现:(1)无套利局部波动率曲面可灵活刻画波动率偏态和期限结构,充分挖掘市场信息;(2)不同时期,上证50ETF期权波动率曲面性态不尽相同,具体表现为NALVS算法下波动率参数的时变性;(3)NALVS算法比BS模型和GARCH模型在场外期权复制对冲上能够得到更小的对冲误差,表明该算法更有利于金融机构对场外期权进行复制和静态对冲。

Based on SVI function, Flat-future interpolation and Dupire formula, this paper proposed NALVS algorithm for Local Volatility modeling, solving the problems of"ExistenceofArbitrage"and"Lack of Data"in Chinese option market by establishing the Arbitrage-free Local Volatility Surface for SEE 50 ETFoptions. The main findings are as followed:(1) Arbitrage-free local volatility surface can flexibly depict volatility skewness and term structure, and fully tap market information.(2) In different periods, the shape of SEE 50 ETF option market’s local volatility surface are different, which can be implied from the time variant of volatility parameter under NALVS algorithm.(3) The NALVS algorithm can get smaller hedging error than the BS model and the GARCH model on OTC option replication and hedging, which shows that the NALVS algorithm is more conducive for financial institutions to replicate and hedge OTC options.