Research On Calibration Method Of Financial Rough Stochastic Volatility Model Based On Neural Network

The stochastic volatility model is an important part of the pricing method of financial derivatives.The accuracy of its parameter setting is the key factor and the first condition for financial institutions to reasonably price and predict the product.The financial market uses the stochastic volatility model to describe the implied volatility surface according to the law of changes followed by the price volatility of financial products.How to accurately describe the implied volatility surface of financial asset prices from financial high-frequency big data has become a dilemma for the development of traditional stochastic volatility models.This problem can be effectively solved by using a rough random volatility model instead.However,due to the non-Markov chain nature of the rough random volatility model,there are many difficulties in calibrating the rough random volatility model by traditional calibration methods.By improving the traditional stochastic volatility model and its calibration methods,it is proposed that the rough stochastic volatility model and neural network calibration method can more accurately describe the implied volatility surface generated by financial product price fluctuations.In response to the above-mentioned problems,this article replaces the classical stochastic volatility model and uses the neural network two-stage calibration method to calibrate the financial stochastic volatility model,which enhances the transparency of the calibration process and not only improves investors' response to market information The speed also helps regulators maintain the order of the financial market.The core content of this paper is as follows:First,the fractional Brownian motion and Hurst parameters are introduced to construct a rough random volatility model.In this study,a rough stochastic volatility model was constructed by improving the general stochastic volatility model and introducing fractional Brownian motion and Hurst parameters.The rough stochastic volatility construction financial asset pricing model has a higher accuracy in describing the law of financial asset price volatility than the general stochastic volatility model,which can better cope with the large amount of high-frequency data generated by high-frequency trading in the financial market and overcome The general stochastic volatility model cannot effectively fit the short-term memory behavior of high-frequency data,and can judge market trends through the roughness of model parameters.Then,the method of generating sample data is improved by proposing the use of Latin hypercube sampling technology.Aiming at the problem of uneven coverage of sample distribution,a Latin hypercube sampling method is proposed to replace the traditional method of randomly generating sample data.This method of generating sample data will make the distribution of the generated samples more reasonable,thereby making the neural network model calibration result more accurate.Finally,the application of the neural network two-stage calibration model is expanded.The use of neural network to calibrate the rough random volatility model has advantages over traditional calibration methods in terms of time,efficiency and accuracy.However,the application of the neural network calibration method to the calibration of the rough random volatility model is still in the exploratory stage,and there is currently no target The rough Heston model is used for the research of neural network calibration.Therefore,the paper will introduce the neural network two-stage model calibration method to calibrate the rough Heston model,so as to achieve a more efficient rough Heston calibration method.This paper studies and explores the neural network model combined with the calibration method of the LM(Levenberg-Marquarelt)algorithm and the basic principles of the Markov chain Monte Carlo calibration method,and discusses and analyzes the main parameters of the calibration of the financial rough stochastic volatility model based on the neural network and MCMC Process;Finally,two methods are used to conduct empirical analysis on two rough stochastic volatility models of finance,and to compare and analyze the four calibration results of two rough stochastic volatility models.This paper summarizes the relevant domestic and foreign literature and the theoretical analysis and empirical research involved in the research and analysis of this article,and draws the following conclusions: First,in theory,the two-step neural network calibration method used in the rough stochastic volatility model calibration can be Effectively solve the problems of low efficiency and speed in traditional calibration,and help solve the network black box problem of general neural network calibration.Second,the empirical research results show that the neural network calibration method has higher accuracy,faster time and stability in the calibration of the rough random volatility model than the traditional calibration method.