Estimation Of Risk Neutral Probability In The Binomial Model

With the innovation of the global financial market, the kinds of financial derivatives become more and more. Option is one of them,which plays an important role in the financial derivatives, and It has particular function in coping with and managing risk,compared with others. At the same time, options also become active in the Chinese mainland market with domestic capital market getting better.Option pricing is always one of the important issues in different studies like Finance.Option price is the fund that the buyers should pay to sellers for obtaining the right in the contract. in order to avoid risk and hedging for both buyers and sellers,we need to explore the option price.This article is mainly about the risk-neutral probability P which affects binomial pricing model. First, considering that the return on the underlying assets is volatile, and combining with the chebyshev law, we use the following methods respectively to estimate fluctuation range of the risk-neutral probability: assuming the function X and Y of random variable ascending and descending multiplier independent distributed in Beta, estimating the density function of P according to the nonparametric kernel density method and simulating the distribution function of P with the functional approach of the BP neural network function.Next, in accordance with the real options data of 50 ETF from June to December in2015, this article proceed the simulation and comparison of the different results of fluctuation range of P by the methods above, the numerical result show that, It’s a ideal range estimation method that we assume the functions X and Y is independent distributed in Beta,which can provide references of options pricing for buyers and sellers.