单指标非参数期权定价——改进的非参数定价方法

本文建立一种改进的非参数期权定价模型，称为单指标非参数期权定价模型。相比现有非参数回归期权定价模型是期权价格关于各个因素的多元回归函数，本模型通过变量变换把期权价格多个因素指标转换为一个综合变量——单指标，得到期权价格关于单指标的一元非参数回归方程。改进的模型实现了多元非参数期权定价模型的降维和简化了模型计算；还通过多个期限期权的单指标组合解决了非参数估计的样本数量问题；以及通过期限平滑解决了现有非参数定价模型中的日历效应问题。选取上证50ETF期权数据实证分析表明，无论是样本内的估计结果还是样本外的预测结果都比传统的Black-Scholes模型、半参数Black-Scholes模型和多元非参数回归期权定价模型估计效果有提高。

Single-index Nonparametric Option Pricing Model——A Modified Nonparametric Pricing Approach

Recent years, the derivatives market developed rapidly in China. The SSE 50ETF option was introduced in February 2015, which is the first stock option in China. The number of the options are 14 by the end of the year of 2019 in China. Option is one of the most active product in financial market, and the investment risk in financial market can be hedged by option, and the option price estimated exactly is the fundament of risk hedge. However, the existing pricing models all are based on the developed financial market, and the financial circumstance is different between developed market and emerging market. As the option emerging market, pricing error will be great if we price option in China with existing pricing model, so this thesis establishes a new nonparametric option pricing model, the so-called modified nonparametric option pricing model which we called the single-index nonparametric option pricing model.The problem of estimating and conducting inference on the term structures of a class of economical interesting option portfolios is considered. By forming portfolios for various maturities, we can study the term structure can be studied. Also, option have different liquidity with different maturity, as we all known, the liquidity will affect the option price. However, the existing nonparametric regression option pricing models have omitted the term structure of different maturities.Compared with the existing multi-dimension nonparametric regression option pricing model that option prices about multi-factors, our modified model combines all of the factors of option price for one factor (the so-called single-index) by changing of variable, finally we get the one-dimension nonparametric regression equation between option prices and the single-index. Our new nonparametric option pricing model has three advantages subject to the existing nonparametric option pricing models, the first advantage is that the multi-dimension nonparametric regression option pricing model is reduced for one-dimension nonparametric regression option pricing model, so that the option price can be computed conveniently, the number of repressors and the computation of the existing nonparametric option pricing model can be reduced. The second advantage is that, the number of regression sample is additive by indexing options portfolio of multiple maturities. The third advantage is that calendar Spread can be removed by indexing smoothing option of maturities.The SSE 50 ETF option is listed in Shanghai Stock Exchange in 19 February 2015, which is the first stock option in China, so this thesis makes empirical analysis by the data of SSE 50 ETF option in Shanghai Stock Exchange, it is found that our single-index nonparametric model performances better than traditional Black-Scholes model, semi-parametric Black-Scholes option pricing model, multi-dimension nonparametric regression option pricing model whether in-sample or out-of-samples data, such as, for in-sample data, the MAE of traditional Black-Scholes option pricing model is 0.4594, the MAE of multi-dimension nonparametric regression option pricing model is 0.2423, the MAE of semi-parametric Black-Scholes option pricing model is 0.2336, the MAE of the our single-index nonparametric model is 0.0845.Our new nonparametric option pricing model will pricing exactly for option in China and other emerging market, and can be the conference for option pricing theory and models.