| For a long time,investors’ management of volatility has been the focus of investment strategies.Reasonable volatility management enables investors to resist abnormal market fluctuations and firmly implement investment strategies.With the launch of stock index options on December 23,the dependence of option prices on the volatility of underlying assets makes the volatility issue more and more concerned by the market.Volatility derivatives are financial products that can directly and effectively manage volatility positions.This paper studies the widely traded variance swaps in the over-the-counter market,with the underlying asset is the S&P 500.Through the empirical study of the variance swap,the prediction performance and advantages of Heston model,Poisson model and Hawkes model were compared,and the parameter estimation was assisted by option data to overcome the problem of insufficient variance swap data and improve the stability of estimation.Firstly,this paper introduces the basic financial knowledge and theorems about option pricing and variance swap pricing,as well as the development of finance model.The theoretical values of option and variance swap corresponding to the three models are given and their characteristics are analyzed.Then,the data was preprocessed,and there was a small amount of missing in the variance swap data.The accuracy of missing value filling was improved by weighted average interpolation in the horizontal time series direction and regression interpolation in the maturity direction.Option data improves data quality by eliminating options data that too far or too near to the maturity date and too large the gap between the strike price and the underlying asset price.Above steps screen out the optimal data for the model.Next,the option and variance swap data were used for parameter estimation.The option data were not predicted,and all of them were taken as training sets.The variance swap data took the data with maturity of 1-18 months as training sets,and the data with maturity of 24 months as test sets.For Heston model and Poisson model,we use the option data at each time point to estimate the parameter,take the parameter as the initial value,assign the value to the objective function of variance swap data,and search.For Hawkes model,since we do not know the analytical solution of the option under this model,we use the parameter estimation result of Poisson model as the initial value.Finally,we conducted sensitivity analysis,error analysis,and establish infectious risk indicators for the model,sensitivity analysis including the sensitivity of the sampling frequency and the sensitivity of the parameters.The former gives us a theoretical basis to use sparser data for prediction in practice.The latter proves that the random volatility part and the Hawkes jump part of the Hawkes model have significant effects on improving the prediction accuracy.In the error regression analysis,we carry out multiple regression to the error and analyze the relationship between the error and the corresponding factors.In terms of the index of infectious risk,the relationship between the index of infectious risk and relevant macroeconomic indicators is verified by regression analysis,and the rationality and effectiveness of the index are verified。... |
