VIX期权定价研究参数与非参数方法的比较

发布时间：2018-01-26 15:49

本文关键词： ⅤⅨ期权设定检验参数估计风险中性概率测度正则定价　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：波动性是金融市场的基础特征,市场波动率如果始终保持不变,说明整个金融市场交易几乎停滞,但是如果波动率过大又缺乏相应的风险对冲工具,投资者又会因为担心风险而放弃交易。作为刻画金融市场隐含波动率的工具,VIX期权自推出以来就受到广泛欢迎,同时在CBOE交易所中交易量越来越大。为了实现良好的市场风险对冲效率,VIX期权定价模型的选择非常重要。在传统的VIX期权参数定价方法中,如果选择的定价模型能够较好的刻画出VIX指数价格运动规律,以此为基础进行参数定价,计算出的VIX期权理论价格和市场价格较为接近,从而实现良好的对冲效率。但是由于VIX期权参数定价方法建立在假设分布的基础上,同时假设条件较为严格,现实的市场因素有时无法满足理论的假设条件,从而造成VIX期权理论价格严重脱离真实的市场价格,因此可以考虑利用非参数定价方法针对VIX指数进行期权定价。本文首先选择了四个经典的VIX期权定价模型进行定价研究,即几何布朗运动模型、平方根均值回复模型、对数均值回复模型、对数均值回复跳模型。然后针对这四类定价模型进行设定检验分析,通过广义残差拟合优度检验方法考察四类模型的检验情况,以此验证定价模型对VIX指数数据的拟合效果,然后在此基础上进行VIX期权参数定价分析,在设定检验分析中,最核心的是计算四类模型的转移概率密度函数,特别的,可以利用Hermite多项式方法计算得出对数均值回复跳模型的转移概率密度的近似表达式。进一步,针对四类模型进行参数定价研究,此时VIX期权的理论价格可以表示为参数模型漂移项和扩散项的泛函表达式,依据无套利定价或者风险中性定价理论分别推导出四类VIX期权的定价公式,同时考虑相应的参数估计方法分别估计出模型的参数值,分别代入期权泛函表示式中,计算可得VIX期权定价模型的理论价格。再考虑VIX期权的非参数定价方法,如正则定价方法,利用风险中性定价原理,推导出仅仅依赖VIX指数历史价格数据的非参数定价公式,并进一步结合另一个期权价格信息,推出更为精确的VIX期权定价表达式,VIX期权正则定价方法中最核心的部分在于将真实的概率测度转化为风险中性测度,由此可得VIX期权非参数价格。最后,编写相应的matlab程序进行数据分析,通过模拟分析和实证分析,分别比较VIX期权的市场价格、参数模型的理论价格和非参数价格。
[Abstract]:Volatility is the basic characteristic of the financial market. If the volatility of the market remains unchanged all the time, the whole financial market almost stagnates, but if the volatility is too large and lacks the corresponding risk hedging tools. Investors will give up trading for fear of risk. VIX options, a tool for characterizing implied volatility in financial markets, have been widely welcomed since their launch. At the same time, the trading volume in CBOE exchange is increasing. In order to achieve good market risk hedging efficiency and the choice of VIX option pricing model is very important. In the traditional VIX option parameter pricing method. If the selected pricing model can better depict the VIX index price movement law, on the basis of the parameter pricing, the calculated VIX option theory price and market price are close to each other. But because the VIX option parameter pricing method is based on the hypothesis distribution, and the assumptions are more strict. Sometimes the realistic market factors can not meet the theoretical assumptions, thus causing the VIX option theory price to deviate from the real market price seriously. Therefore, we can consider using non-parametric pricing method to price VIX exponent. Firstly, four classical VIX option pricing models are selected for pricing research, namely geometric Brownian motion model. Square root mean recovery model, logarithmic mean recovery model, logarithmic mean recovery jump model. Through the generalized residual goodness of fit test method to investigate the test of four kinds of models, so as to verify the effect of the pricing model on VIX index data, and then carry out the VIX option parameter pricing analysis on this basis. In the set test analysis, the core is to calculate the transfer probability density function of four kinds of models, especially. Hermite polynomial method can be used to calculate the approximate expression of the transfer probability density of the logarithmic mean recovery-jump model. Further, the parameter pricing of four kinds of models is studied. At this time, the theoretical price of VIX options can be expressed as the functional expressions of the drift term and diffusion term of the parametric model. According to the theory of no-arbitrage pricing or risk-neutral pricing, the pricing formulas of four kinds of VIX options are derived respectively. At the same time, the corresponding parameter estimation methods are considered to estimate the parameters of the model, respectively, into the option functional expression. The theoretical price of VIX option pricing model is calculated, and the non-parametric pricing method of VIX option, such as regular pricing method, is considered, and the risk-neutral pricing principle is used. The non-parametric pricing formula which only depends on the historical price data of VIX index is derived, and a more accurate VIX option pricing expression is derived by combining with another option price information. The core part of the regular pricing method of VIX options is that the real probability measure is transformed into the risk neutral measure, and the non-parametric price of the VIX option can be obtained. Finally. The corresponding matlab program is written for data analysis. Through simulation analysis and empirical analysis, the market price of VIX option, the theoretical price of parametric model and the non-parametric price are compared respectively.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9

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