Nonparametric Estimates On Evaluating European Options Value

The key factor of options pricing is the distribution of the ultimate stock prices. When built the B-S formula in the complete market, the stock prices are assumed to obey geometry Brownian movement, however, it is inconsistent with the results of the substantial evidence to be tested, so the options pricing in the incomplete market can't be assumed to obey geometry Brownian movement. As not to know the stock prices obey what distribution, we accord to historical data to estimate the distribution of the ultimate stock prices by kernel density estimation, then develop the theorems for options pricing, and price the option. The following is the studying process on the problem.First of all, we overview the methods of the option pricing and the compute, then make the tests of normality on the return rate of stock by skewness-kurtosis test and Kolmogorov-Smirnov test. The results show that the stock return rate doesn't obey normal distribution, thus the ultimate stock prices don't obey geometry Brownian movement.When the ultimate stock prices don't obey geometry Brownian movement, we consider how to price the options. When don't know what distribution the stock prices obey, we accord to the historical data to estimate the distribution of the ultimate stock prices by kernel density estimation. Since the return rate has the character of repeat coming in its lifetime, we directly study the distribution of the return rate X n, then change it into the ultimate stock prices by the formula XnS T = Se, and accord to the theorem 5 to price the options. Because the return rate has many good characters such as the following, we estimate the return rate by use of the characters.Theorem 1[20] Set kernel function K (u) and density function f (x) satisfy the following conditions:...