Option Pricing With Liquidity Risk Based On Nonlinear Expectation

The process of financial crisis is often accompanied by the lack of market liquidity.One of the most direct manifestations of financial crisis in the market is the sharp fluctuation of asset prices,and the lack of market liquidity will lead to significant price changes in transactions.As an important part of the financial market,option is often used by investors to hedge risks and improve returns,but also stabilize the market economy.However,when the underlying asset market of the option is short of liquidity,the price of the corresponding option will also be affected.Therefore,adding liquidity risk factors into the option pricing model has important reference value for making the option pricing model closer to the real financial market.When the market contains liquidity,it can no longer meet the perfect market hypothesis of the classical B-S-M option pricing model.Therefore,this paper firstly introduces liquidity risk factors on the basis of the classical B-S-M option pricing model,and then makes use of nonlinear expectation theory under the assumption of incomplete market.By defining the fuzzy coefficient η,the uncertainty of return rate and volatility is represented in the form of interval so that the risk-neutral measure can be extended to the equivalent martingale measure family.Then,the maximum and minimum price pricing formula of European call option with liquidity risk is obtained by calculation of expectation and empirical test is carried out.The results show that compared with the nonlinear expectation pricing model without liquidity risk,the pricing formula of liquidity risk introduced in this paper is closer to the real financial market.For option pricing in the incomplete market,the maximum and minimum price pricing method can give the option price range through the maximum and minimum price.Therefore,subsequent studies are devoted to narrowing the range of maximum and minimum prices to more accurately approximate the real market price.The innovation of this article is mainly manifested on the one hand was deduced based on nonlinear expected to contain the liquidity risk of European option pricing formula,generalize the liquidity risk in European option pricing model,on the other hand on the European call option on the process of numerical simulation,using the method of sliding window to estimate the uncertainty of the returns to ensure returns,The results show that the introduction of liquidity reduces the fuzzy interval and improves the accuracy of the model.