State The Price Of Nonparametric Density Estimation

State price density is a kind of financial risk measurement, it is a sufficient statistic of derivative securities pricing. It focuses on all information of the preference and business conditions about pricing. What’s different from option pricing formula is Option pricing formula theory is up to a variety of options payment function, however, state price density is on behalf of density of the same underlying assets under the risk neutral measures, and it has nothing to do with options payment function. So the estimator from one kind of option price can be used to calculate another derivative securities under the same underlying assets. Such as, we can price American option according to state price density calculating from European option. In this regard, non-parametric estimation of state price density is very significant.In this paper, we carry on research of non-parametric estimation of state price density based on European call option, whose underlying assets is CF Industries Holdings, Inc.This paper’s mainly work is as follows:Part1, we mainly introduce the existence of state price density and the research status of non-parametric estimation of state price density. Part2, we mainly introduce the construction and improvement of non-parametric estimator of state price density. Part3, we carry on simulation analysis, we estimate state price density by local polynomial regression and additive model, and comparison with formula value. Part4, we make the empirical analysis, we estimate the real state price density based on option price. Part5, conclusion. According to simulation and empirical analysis, we made a conclusion that additive model is a good method of non-parametric estimate of state price density. What’s more, we proved the rationality of option pricing by Black-Scholes formula from the point of view of state price density.