Pricing Of European Options With Risk-neutral Moment

Option pricing is not only an important research content in the financial field,but also the core of modern finance.In 1973,Black and Scholes gave a famous option pricing model under a series of assumptions that the volatility is constant,the market is complete,and the underlying asset price follows a log-normal distribution.However,these assumptions are somewhat different from the real market situation.As a result,the option pricing results are not ideal.The options market contains a lot of useful information for option pricing.In order to reduce dependence on existing models or assumptions,we need to extract information from the real market that is effective for option pricing.The entropy pricing model proposed by Stutzer in 1996 became one of the nonparametric models for option pricing.Later scholars found that the KL distance used by Stutzer is a special case in the Cressie-Read family.Even if the market is incomplete,the effective information of the market can be used to extract the risk neutral moment through the entropy theory,and then the target asset price distribution probability that matches the real market can be obtained.The risk neutral moment extracted from the actual market does not depend on models and assumptions,so the entropy pricing model based on risk neutral moment can effectively price options.This paper builds a model of five distance functions embedded in the CressieRead family in the risk neutral moments,and further tests the validity of the entropy pricing model based on the risk neutral moments in the BS environment.The European option price under the BS model is used as a benchmark.The analysis of the general entropy pricing model shows that the exact pricing can be given in all cases except T = 1/12,which is almost comparable to the BS formula.Moreover,the pricing error of the entropy pricing model based on risk neutral moments decreases with the rise of Moneyness.When five types of entropy pricing models are used to price call and put options,the difference between the pricing error of call and put options is not obvious.Finally,the validity of the generalized entropy pricing model is further tested under the Heston environment.Based on the pricing results of European options under the Heston model,the analysis results show that the five entropy pricing models based on risk neutral moments can effectively capture the real market useful information for option pricing.