Research On Option Pricing Model Construction And Parameter Parameter Estimation

Option is one of the most active risk management tools in the global capital market.How to determine the fair price of option is a key to its reasonable existence and healthy development.In 1997,the Nobel Prize in economics was awarded to Scholes and Merton,the inventors of the option pricing formula,which embodies the affirmation of the theoretical value of option pricing in the economic circle.Since the B-S model came out,it has aroused strong repercussions in the academic and practical circles.While widely used,scholars have carried out in-depth tests on its accuracy,and through a large number of empirical studies found that the market does not meet the ideal basic assumptions.Many economists reexamine the original theory of mathematical finance and express different views on the problems existing in the model,and carry out a lot of extended research from the perspective of improving and developing the B-S model.In recent 30 years,the improvement of B-S model has become a hot topic in the field of mathematical finance.It greatly improve the theory and method of option pricing,but there are still some shortcomings.Based on the literature review,this paper finds four shortcomings in the existing research:(1)research on parameter estimation,the improved model usually contains many parameters to be estimated,and the objective function contains a large number of extreme points,which makes parameter estimation difficult.Current research mainly uses maximum likelihood estimation method to estimate the parameters of option pricing model,but there are many problems that are difficult to solve.(2)The research on parameter estimation method of option pricing model under high frequency quantitative trading is very scarce.(3)Local volatility models mostly rely on subjective experience to model volatility using time and asset prices as influencing factors.Although these models are easy to understand and explain,they often deviate from the actual situation in accuracy,and there is no theoretical basis for which form is reasonable,resulting in poor robustness of the models and weak ability to describe the abnormal volatility of violent motion.(4)Whether volatility model or jump diffusion model is usually a single model in form,the ability to depict volatility "smile" is insufficient,resulting in large deviation in the pricing of deep real value and deep virtual value options,resulting in unstable pricing.To overcome these shortcomings,solid and advanced mathematical and physical methods must be indispensable.The characteristics and performance of deep learning,integrated learning and intelligent optimization algorithm make it widely used in various fields of artificial intelligence,and also provide a solid and reliable tool for quantitative research of financial derivatives.Therefore,this paper discusses option pricing from two aspects of parameter estimation and model construction based on deep learning,integrated learning and intelligent optimization algorithm.This paper is mainly engaged in two aspects of research work.In the first part,the research on parameter estimation of option pricing model:according to the demand of middle and low frequency quantitative trading,design genetic algorithm to estimate the parameters of Heston option pricing model;according to the demand of high frequency quantitative trading,use the previously designed genetic algorithm to accumulate the historical case solution information,then design two-stage heuristic algorithm to estimate the model parameters based on convolution neural network.In the second part,the research of option pricing model construction:in order to improve the stability of model pricing,the Heston model obtained in the first part is used as the basic learner to build the composite option pricing model based on the integrated learning;in order to improve the robustness of the model,the deep Boltzmann machine and support vector machine are used to build the volatility function with the goal of structural risk minimization.The research proceeds step by step.The parameter estimation method for low-frequency trading is the premise of the parameter estimation method in high-frequency trading,and the results of the first part of the parameter estimation are the basis of the second part of the model construction,which provides a basic learning machine and training method for the modeling process.The research results and core contents are as follows:Research on parameter estimation of option pricing model:(1)According to the low-frequency quantitative trading demand of options,the first deposit genetic algorithm is designed to estimate the parameters of Heston option pricing model.The algorithm has the characteristics of avoiding losing the optimal solution and parallel search,and has a good probability to jump out of the local minimum and converge to the global minimum with probability 1.In the calculation experiment,the trading data of Hong Kong Hang Seng stock index options are used as samples to obtain the parameters to be evaluated,and the call options and put options in the prediction period are simulated and priced with this parameter.The numerical results and evolution process show that the algorithm takes time to meet the real-time requirements of the low-frequency quantitative trading strategy in options,the pricing accuracy on the training sample data set is high,and the simulation pricing accuracy on the prediction period is satisfactory,which overcomes the shortcomings of the traditional algorithm to a certain extent.(2)A two-stage heuristic algorithm based on convolutional neural network is proposed to estimate the parameters of option pricing model.The core idea of the algorithm is to accumulate the historical information on the training examples with the genetic algorithm designed before,generalize and learn it based on the convolution neural network,and guide the PSO algorithm to solve the new examples with the generalization results of the new examples.In the calculation experiment,the Heston model is taken as an example,and the 1-minute high-frequency trading data of 50ETF options are used.The numerical results show that:? the convolutional neural network designed in this paper can complete the off-line learning of nine main contracts well,and the average relative error on the training data set is 24%.If the traditional neural network is used,the error is huge and does not converge;?the algorithm in this paper can use of historical data information to efficiently solve new cases,and under the guidance of convolution neural network,the PSO optimization stage can reach convergence in about 8 seconds,meeting the real-time requirements of high-frequency quantitative transaction analysis;? the model pricing based on the obtained parameters has high consistency with the actual price.The algorithm is feasible and effective.Research on option pricing model construction:(3)In order to improve the stability of model pricing,the pricing model of portfolio options is built based on integrated learning,which improves the pricing accuracy of the model for deep real value and deep virtual value options.In this paper,Heston model is used as the basic learner,and AdaBoost algorithm is used to train a series of basic learners and integrate them.The parameter estimation is decomposed into the main problem and the subproblem.Based on the idea of the recommendation algorithm and the genetic algorithm designed before,the algorithm is given.By calculating the average relative error and the stability deviation(this paper defines the stability deviation of model pricing as the difference between the maximum relative error and the average relative error),the pricing ability of this model and the traditional model is compared and analyzed.The results of two groups of calculation experiments on the contracts expiring every other month and the current month show that,compared with the traditional Heston model,the portfolio option pricing model keeps the average relative error basically consistent,while the stability deviation is reduced by 64%and 49%respectively,which can make the option pricing of all execution prices reach the preset stability standard.This research enriches the research methods of option pricing and extends the application boundary of integrated learning.(4)In order to improve the robustness of the model and the ability to distinguish complex laws,this paper uses deep Boltzmann machine to extract the influencing factors of volatility automatically,scientifically and effectively.Based on this,a deterministic volatility function model with the goal of minimizing structural risk is built by using support vector mechanism,and the solution of the model is transformed into a nonlinear programming problem with only linear constraints.The results show that the average absolute error and the average relative error of the SVM model on the 50ETF option historical volatility training samples are reduced by 70.86%and 77.89%respectively by data feature extraction.The shortcomings of the traditional methods such as manual design of influence factors,ignoring the confidence range of the model are partly solved,and the ability of the model to describe abnormal volatility is improved.