VIX Option Pricing Research Comparison Of Parameters And Nonparametric Methods

Volatility is a fundamental feature of financial markets.Market volatility,if it remains constant,suggests that the entire financial market is almost stagnant,but if volatility is too large and there is a lack of risk hedging tools,investors will abandon the transaction for fear of risk.As a tool to characterize implied volatility in financial markets,the VIX option has been widely welcomed since its introduction and has been increasingly traded on the CBOE.In order to achieve good market risk hedging efficiency,VIX option pricing model selection is very important.In the traditional VIX option pricing method,if the selected pricing model can better describe the price pattern of motion of VIX index,The difference of VIX option theory price and market price is small,so hedging efficiency is good.Because the VIX parameter pricing method is based on the hypothesis distribution and the assumption is more stringent,the real market factor can not meet the theoretical hypothesis.Therefore,it can be considered to use the non-parametric pricing method for VIX index option pricing.In this paper,four classical VIX option pricing models are selected for pricing research,namely Geometric Brownian Motion Model,Square Root Mean Reversion Model,Logarithm Mean Reversion Model and Logarithm Mean Reversion Jump Model.Then test the four types of inspection models to verify the VIX index data fitting effect with models through the generalized residuals goodness of fit.Then the pricing of VIX option is analyzed on this basis.In the setting test analysis,the calculations of transition probability density function of four models is the most important.In particular,the polynomial method can be used to calculate the approximate expression of the transition probability density of the log-mean regression model.Furthermore,the theoretical option prices of four VIX models can be expressed as the functional expression of drift term and diffusion term of models.Based on no-arbitrage pricing theory or risk-neutral pricing theory,deduce the pricing option formula of four models,then estimate the parameter values of model with corresponding parameter estimation method and calculate option theoretical price of four VIX models.Further,considering the non-parametric pricing method of VIX options,such as the regular pricing method which relies on the historical price data of VIX index,deduce non-parametric pricing formula by using the risk neutral pricing principle,and another option price information is introduced.The most important part of VIX option regular pricing method is to translate the real probability measure into the risk-neutral measure,then calculate the non-parameter price of the VIX option.Finally,matlab program is written for the empirical and simulation analysis,comparing market price of VIX option,theoretical price of four models and non-parametric price respectively.