Research On The Option Pricing With Liquidity Risk

Options,as an acknowledged risk management tool,can better hedge risks and effectively guide market participants to make investment decisions.With the approval of the China Securities Regulatory Commission,SSE 50 ETF options was listed on the Shanghai Stock Exchange on February 9,2015,which was the first option contract in Mainland China.The listing of the SSE 50 ETF options not only marks the arrival of the Mainland China option’s era,but also means that a new era of diversified investment and risk management is coming.On the other hand,with the continuous expansion of global financial product innovation and market size,both the uncertainties in the global economic environment and the volatility of financial markets have also gradually increased.In recent decades,the global financial market has frequently experienced liquidity crisis.At present,a large number of empirical studies have shown that the liquidity is an inherent characteristic of the financial asset and is closely related to the assets return.Thus,it is particularly urgent and important to consider the influence of these realistic factors and to propose a reasonable option pricing model combined with the sample data of the Chinese option market.However,the classical option pricing theories are usually built on the paradigm of a perfect financial market,and it is difficult to explain the imperfection of the real market.In recent years,many scholars have begun to try to introduce the liquidity and other microstructure factors into the underlying asset price process,and then study the option pricing problems.At present,this research work is slowly progressing and is still at an exploratory stage.Therefore,this paper will comprehensively use the liquidity premium theory,modern financial economics,mathematical finance,stochastic analysis and other methods to study the option pricing problems that in illiquid market.And collect as much sample data as possible for empirical analysis.The main researches and contributions of this thesis are summarized as follows:First,a liquidity-adjusted stochastic volatility model is proposed,and the corresponding European option pricing formula is derived.The existing stochastic volatility models usally assume that the market is both frictionless and perfectly liquid,while ignoring the impact of market liquidity risk on the underlying asset prices.Hence,this thesis proposes a liquidity-adjusted stochastic volatility model by the liquidity discount factor to describe the dynamics of the underlying asset prices.And then,an analytical approximate pricing formulas of the European options are derived by using the Fourier cosine series expansion.Finally,we empirically investigate the effect of the proposed model on the pricing accuracy of SSE 50 ETF options.By comparing the proposed liquidity-adjusted stochastic volatility model with the classic Heston model,we find that the former is strongly superior to the latter in both in-sample and out-of-sample pricing errors.Moreover,these results are robust for different error metrics and liquidity measures.Second,under the assumption that the underlying asset price follows the liquidity-adjusted Black-Scholes model,the analytical pricing formulas of the continuously monitored geometric Asian options are derived.Meanwhile,we also present the put-call parity relations for the continuously monitored geometric Asian options.The existing Asian option pricing models are usually built on the paradigm of the perfectly liquid market.Considering the impact of market liquidity risk on the underlying asset price,this thesis first supposes that the dynamics of the underlying asset prices follow the liquidity-adjusted Black-Scholes model^[88],and then derives the partial differential equation for the continuously monitored geometric Asian options based on the delta-hedging strategy.Furthermore,the closed-form solutions for the continuously monitored geometric Asian options are derived by variable transformation method,and the put-call parity relations for the continuously monitored geometric Asian options are also presented.Third,a liquidity-adjusted jump-diffusion model is proposed,and the analytical approximate pricing formulas for the discrete barrier options are derived.Therefore,this thesis proposes a liquidity-adjusted jump-diffusion model to describe the dynamics of the underlying asset prices.Financial markets are usually affected by many uncertainties,such as financial crisis,inflation,liquidity shortage and among others.Once these events occur,the value of financial assets will often be drastically reduced,which will cause a jump in asset prices.Moreover,considering that the real market trading usually is the discrete barrier option,this thesis present the analytical approximate pricing formulas of the discrete barrier options by using the COS method,and the corresponding solution algorithm is also presented.Finally,to investigate the accuracy and convergence speed of the analytic approximate pricing formulas,we implement numerical analysis by Monte Carlo simulation.Fourth,a liquidity-adjusted quanto model is proposed,and the analytical pricing formulas for four different types of European quanto options are derived.With the growth and deepening of global economic integration and the integration of financial markets,the quanto options,as a risk management tool for investing in foreign risk assets,have gained wider popularity among investors.The existing quanto option pricing models are usually built on the paradigm of the perfectly liquid market,while ignoring the impact of market liquidity risk on the foreign underlying asset prices.Therefore,under the assumption that the market is imperfectly liquid,this thesis proposes a liquidity-adjusted quanto model,and then derives the analytical pricing formulas for four different types of European quanto options by utilizing the risk-neutral pricing principle and equivalent measure transformation.Finally,we empirically investigate the pricing performance of our proposed quanro model with a European quanto option construction involving the SSE 50 ETF,as the underlying asset,and the CNY/HKD exchange rate.Empirical results demonstrate that the pricing accuracy of the proposed models is markedly superior to that of the Black-Scholes quanto model.Particularly,the improvement rate is high for out-of-money and medium-term options.Moreover,these results are robust for different liquidity measures.