Research On Option Pricing And Hedging Strategies Based On Liquidity Incomplete Market Conditions

In modern financial markets,options are the most widely used financial derivatives when hedging.With the approval of the China Securities Regulatory Commission,SSE 50 ETF options was listed on the Shanghai Stock Exchange on February9,2015,which was the first option contract in Chinese mainland.So far,it provides a new idea for financial derivatives trading and the design of hedging strategies in China.In addition,it also increases the liquidity risk in the financial market as the uncertainty of the global economic environment intensifies.At present,a large number of empirical studies have shown that there is an inseparable relationship between asset liquidity and its prices.Therefore,only the influence of liquidity factors is taken into account in option pricing may the accuracy of hedging be improved and the risk can be accurately avoided.In recent years,several scholars have introduced liquidity factors into the pricing process of financial derivatives,but the research results are relatively small.Therefore,this paper will use the theory of Esscher transformation to study the option pricing and hedging strategy under the condition of incomplete liquidity market.The main innovations of this paper are summarized as follows:(1)Based on the liquidity adjusted asset pricing formula,the explicit expression of the call digital power option pricing formula is given using the Esscher transformation theory.The improvement compared to other call option pricing processes is that instead of calculating the unique h in the Esscher transformation theory,we only need to calculate the mean and variance of random variables.Then,based on the S&P 500 Index,the unknown parameters and ζ are estimated using Bayesian statistical inference and Monte Carlo numerical integration methods,and a posteriori inference is performed on the option price.The empirical results show that when the financial market environment fluctuates greatly,it is di cult to estimate the unknown parameter ζ.In order to verify the impact of asset liquidity on option pricing,we simulated the option price of the underlying asset with and without considering liquidity factors.By comparing the simulation results,we found that the option price considering asset liquidity risk is more accurate.At the same time,it also indicates that our pricing formula is more practical compared to traditional option pricing models.(2)Considering the case where asset prices follow a jump diffusion process,a jump factor is added to the explicit expression of the call digital power option pricing formula.After calculation,it is found that the explicit expression of the call digital power option pricing with diffusion process can also be obtained by calculating the mean and variance of random variables.Through numerical simulation using MATLAB software,the results still show that option prices are sensitive to changes in power indices(3)Based on the obtained display expression of the call digital power option pricing formula,using the same principle,the display expression of the put digital power option price is given.And the value at risk(VaR)is used as the risk measure tools to measure the risk of asset and put digital power option portfolios.The numerical simulation using MATLAB software shows that both power exponent and liquidity level have a significant impact on the VaR value.