European Option Pricing Based On Combined Prediction Model With Variable Weight Coefficient

In recent years,the international financial market has become more and more free and connected,the market has become more and more volatile,and the risks faced by market entities have also increased.As an effective tool to hedge risks,option has been paid more and more attention,many scholars devote themselves to option pricing and put forward a series of methods of option pricing.Black and Scholes put forward the Black-Scholes(B-S)option pricing model in 1973 under a series of assumptions.The study shows that the volatility of the underlying price is an important factor affecting the option pricing,and Generalized Autoregressive Conditional Heteroscedasticity(GARCH)model can estimate the volatility of the underlying price series very well.BS-GARCH model is an option pricing model,in which the volatility of the B-S option pricing model is replaced by the volatility estimating by GARCH(1,1)model.The Exponential Weighted Moving Average(EWMA)model uses the volatility which is obtained by exponentially decreasing weighting and then gets the price of option.The Ad hoc Black-Scholes(AHBS)option pricing model is obtained from Fleming and Whaley,who proposed the volatility function by studying the characteristics of volatility.Monte Carlo simulation of stratified sampling is a numerical pricing method that simulates the underlying price path with a better pricing accuracy than the general Monte Carlo simulation.The above four models get the price of option from different angles respectively and have their own advantages and disadvantages,in order to improve the prediction accuracy,we use the combined prediction model to re-price the option.This paper uses the combined prediction model to price the European call option.We select two European call options and divide the data into training set and test set.First,we analyze the historical data and obtain the annual volatility of stock price by GARCH(1,1)model,than,using BS-GARCH model,Monte Carlo simulation of stratified sampling,EWMA model and AHBS model to price the European call options respectively.The pricing effects of the four models on the training set are compared,finally,we select the BS-GARCH model,the Monte Carlo of stratified sampling and the AHBS model as simple model of the combined prediction model,we use equal-weight combined prediction model,the variable weight combined prediction model and the Ba^ck Propagation(BP)neural network model to re-price the option.In order to better compare the pricing effects of different models,this paper proposes a comprehensive index by integrating Variance(VAR),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE)and Mean Absolute Error(MAE).The result shows that the combined prediction model with variable weight coefficient has the best pricing effect for European call option under the new comprehensive index,which is superior to any single prediction model among the combined prediction model,while the combined prediction model based on nonlinear BP neural network has the worst performance.