The Semiparametric Fitting For The Implied Volatility Surface

With the development of financial markets, financial derivatives, including futures, options, also experienced a rapid development, trading volume continues to increase. And how is the pricing of options is a major issue. In 1973, financial professor Black and Scholes, Merton were the basis of this theoretical study, obtained now known as the second revolution in financial option pricing formula (Black-Scholes formula). In options trading, financial risk management, people are more concerned about the performance of volatility, but obviously BS formula is constant on the assumption that volatility is unreasonable. And volatility are relatively accurate it is very necessary.Early study on implied volatility, it is generally regarded as a one variable function of the exercise price or the maturing date, but neglect of both factors'overall impact on the implied volatility. Therefore, taking the implied volatility as a two variables function of the exercise price and the maturing date, and remodeling implied volatility is a very interesting research direction.In this paper, For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a severe modeling bias. We propose a dynamic semi-parametric factor model (DSFM), which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and back fitting techniques for additive models. The model is found to have an approximate 10% better performance than a sticky moneyness model.Innovation of this paper has two aspects, firstly, we proposed a relatively new model on the implied volatility, which played a key role in substantially improved forecast performance;secondly, on the empirical analysis, we overall use the classic models of the implied volatility which used in data processing.In the text of the summary, points out the directions of further research on implied voaltility.