上半方差、下半方差及其不对称性对期权定价的影响

After stock market crash in 2005 in China, the futures market is extremely shrinking while the SSE 50ETF options is still thriving. The volume and the open interest of the SSE 50ETF options have upward tendencies. Apparently, the SSE 50ETF options is more favored by investors to hedge stock positions comparing with the futures. In the following years, with the deepening of China’s financial system reform, more and more options will gradually bring into the financial market of our country. The impact of options market will be more and more important in China’s financial market. Deep research on options has great significance and practical value for the establishment of our country’s options market and making it more standard and perfect.. Generally, overall volatility is used in the traditional option pricing models, while it can’t effectively distinguish the upper risk from the downside risk, resulting in the deviation between the theoretical price and the actual price. This project will focus on the volatility of financial market, and prepare to do some deep research about the problem of option pricing, then analyze the upper semi-variance, the lower semi-variance and the difference (asymmetry) between both, and evaluate their effects on different kinds of options under different factors. The important contribution of this project is to perfect the option pricing models, to make them closer to the real trade, and to provide theoretical basis and instructive guidance for supervisor, investor, trader, and so on in the markets.

2015年股灾之后，中国期货市场出现极度地萎缩，而50ETF期权市场依然欣欣向荣，期权的成交量和持仓量呈现增长的趋势。相比较于期货市场，50ETF期权市场更受到投资者对冲股票仓位的青睐。在未来几年里，随着中国金融体制改革的深入，将会有更多的期权品种逐步进入我国金融市场，期权市场在中国金融市场的影响将越来越大。深入对期权的研究对我国期权市场的建立、规范和完善具有重大指导意义和实用价值。. 传统的采用总体波动率的期权定价模型无法有效区分上侧风险与下侧风险，造成期权定价理论与实际价格之间的偏差。本课题以金融市场波动率研究为着眼点，拟对期权定价问题进行进一步深入研究，重点分析上半方差和下半方差及其差异（不对称性）在不同因素作用下对不同期权价格的影响。通过本项目研究，进一步完善期权定价模型，使理论模型更接近真实交易，为监管者、投资者、交易者等市场参与者提供理论依据和指导性建议。

期权定价是金融工程研究领域的核心问题之一。金融市场的显著特征是具有很强的不确定性。金融资产价格的波动对期权定价有很大的影响。本项目考虑金融市场的不确定性环境，以市场波动率为出发点，围绕上、下半方差及其不对称性，相应引入偏度和峰度，探讨不同类型期权的定价方法和金融风险管理策略。研究内容包括：1）着重考虑了市场波动率的不对称性，建立基于上、下半方差的期权定价模型，实证研究上证50ETF期权的偏度和峰度特征，讨论期权高阶矩在市场风险管理方面的应用；2）理论研究了股票市场的价格形成机理，实证分析了市场交易制度对股票价格波动的影响；3）拓展了现有期权定价理论，提出了几种考虑市场不确定性的期权定价模型，所涉及的理论包括跳扩散过程、矩匹配、模糊随机理论和分数阶微分方程理论等，期权类型涉及欧式期权、美式期权和亚式期权；4）探讨了风险的度量问题，提出了基于二阶正则变分理论和谱风险测度对操作风险进行二阶近似的方法。研究成果可用于设计期权投资策略、风险管理和金融市场监管，具有较好的理论价值和实际应用价值。