Pricing Of Chinese Soybean Meal Options Based On Least Squares Monte Carlo Simulation

Options play a very important role in the stability of futures and spot markets,so the study of options is also very necessary,in which option pricing is an important part.Through combing the research results of previous scholars,it is found that GARCH(1,1)model is the most widely used method in the study of volatility estimation.Meanwhile,EGARCH model and Lévy process take the partial leverage of the conditional variance of the asset yield sequence and the non-normal distribution of the yield sequence itself into account,which has been shown to have a better volatility estimation effect than GARCH(1,1)and is also widely used.At the same time,the pricing effect and maneuverability of the least Squares Monte Carlo(LSM)simulation method are proved to be optimal,so it is widely used in the study of option pricing.In this paper,the reasonable pricing method of soybean meal futures options in China is studied by using LSM to simulate the options corresponding to the M1809 contract of soybean meal futures.The normal test of the continuous price yield sequence of soybean meal futures in September was carried out by using Shapiro-Wilkins test and Anderson-Darling test,and the results showed that the yield of soybean meal futures showed the non-distribution of left thick tail.Besides,the volatility sequence diagram is used to find that there is partial leverage effect on the fluctuation rate of soybean meal futures,and the negative information has more influence on the fluctuation of September-continuous price in soybean meal futures than positive information.In this paper,GARCH,EGARCH and Lévy process are used to simulate the volatility sequence of soybean meal futures,and then the sequence is applied as a parameter to the LSM simulation method.In the choice of risk-free interest rate,this paper selects the average of overnight SHIBOR in the previous year of selected time node.Finally,by setting different path numbers and multiple time nodes to simulate the pricing of 10 soybean meal futures options,the results show that the LSM process with the volatility estimation based on Lévy-EGARCH shows the most pricing result.Meanwhile,the pricing effect of all pricing models will change over time,the closer to the last trading day,the more accurate the pricing results is.However,the impact of the path number setting on the pricing of soybean meal futures options is not significant.And,the LSM simulation method can be close to the real price,but the error cannot be completely eliminated.