Option Pricing Models And Their Application In Risk Management

Option pricing is a hot issue in financial statistics.This article extends the widely used stochastic volatility model,combines the Double Heston model with the Bates model and proposes the Double Heston model with jumps,then combines the Double Heston model with the CIR model,and proposes the Double Heston model with random interest rates.Heston model is proposed on the basis of BSM model,which describes the relationship between asset volatility and asset,and for the first time applies the concepts of "peak" and "asymmetry" into the process of asset return change.Double Heston model substitutes two variance processes into asset changes to simulate the long-term and short-term fluctuations of assets respectively,which fits the market better and is widely used in the field of option pricing.But its limitation is that it fails to consider the market changes when encountering unexpected situations and the asset price changes under the condition of non-constant interest rate.In order to make up for the above shortcomings and apply it to a wider market,this paper puts forward the double Heston model with jump.Referring to the method of introducing jump term in Bates model,the generalized form of the model is obtained by using multivariate Ito formula,Feynman-Kac formula,Fourier transform and other methods,and the semi analytical formula of European call option is given.On the other hand,this paper proposes a double Heston model with stochastic interest rate.Referring to the expression of stochastic interest rate in CIR model,we use the above method to obtain the generalized form of the model,solve the corresponding characteristic function,and give the pricing formula.In addition,option pricing models are also widely used in the field of credit risk assessment.The KMV model is established on the basis of the BSM model.The model puts forward an important conception that the company's credit risk is mainly related to asset value,asset fluctuation and debt ratio.On the debt deadline,if the value of the asset is lower than the company's debt,the company will have a default risk,and the model will play a role in predicting and prompting credit risk based on this.Based on the KMV model,this paper conducts an empirical study on the credit risk of the following two aspects:In the empirical analysis of the debt risk of listed companies,this paper uses the data of 3398 domestic A-share listed companies to improve the default point parameters of the KMV model.Through parameter simulation and actual data inspection,the optimal parameter combination is obtained as DPT=1.60STD+1.30LTD.At this time,the model accuracy rate can reach 90%,and the recall rate is 77%.When discussing the company's subdivision status,it was found that scholars directly used the ST mark to determine the company's breach of contract.The method may be unreasonable;in the empirical analysis of local government debt risk,this article uses the data of 31 provinces across the country from 2010 to 2018 to calculate the growth rate and volatility of government debt service income,and predicts the values of various indicators in 2019 and 2020.According to the model,the default distance and default probability of local governments in various provinces are calculated.The results show that the current default probability of each province is very small,but the performance of each province in the stress test is different.When the government transfer payment is reduced proportionally,Yunnan and Guangxi will take the lead in default risk.Jiangsu,Zhejiang,Guangdong and other places will take the lead when general budget revenue decreases proportionally.When rigid expenditure increases,the default probability in Yunnan,Jiangxi,Hunan and other provinces will greatly increase.In summary,this paper promotes the Heston model in the theoretical research of option pricing,considering the sudden changes in the market and interest rate fluctuations,and adding jump items and random interest rates to the model to make it applicable to a wider range of markets.In the empirical research of option pricing,this paper studied the application of the KMV model.The model was used in the credit risk research of listed companies and local governments.The latest data was used to analyze the domestic credit risk market,and the corresponding conclusions and analysis were given.