The Valuation Of American Options With The Stochastic Liquidity Risk And Jump Risk

Classical option pricing theories are usually built on the paradigm of competitive and frictionless markets,while ignoring the impact of market liquidity on underlying asset prices.In addition,many financial assets,such as stocks,currencies and commodities,usually exhibit jumps,which are particularly prominent in the market after the financial crisis or major incident.In this paper,the stochastic liquidity risk and jump risk of underlying asset are both considered when pricing options.In this paper,we propose a novel model to describe the stochastic liquidity risk and jump risk of underlying asset,and then price American options under this model.When pricing American options,we first derive the analytical expression of the characteristic function of the logarithmic asset price,then price Bermuda options based on Fourier―cosine method,and finally use Richardson extrapolation to get the approximate price of American options.In the numerical experiment,we have carried out the accuracy test and sensitivity analysis.When testing the accuracy,we find that the relative error between the price of Bermuda option and American option obtained by Fourier-cosine method and the result obtained by Monte Carlo method is quite low.Therefore,for the stochastic model proposed in this paper,it is advisable to first derive the analytical form of the characteristic function,and then bring it into the Fourier-cosine method to calculate the option price,and the speed of former is significantly faster.Then in the sensitivity analysis,we only analyzed the sensitivity of American options,because numerical results show that the Bermuda option price is very close to the American option price when the exercisable time point is relatively small.We tested the influence of model parameters on the American option price,and found that the change of parameters would lead to the obvious and regular change of option price,and the change of option price with the change of parameters could find a reasonable explanation for the actual market.Therefore,the experimental results of sensitivity analysis support us to consider the liquidity factor and jump factor into the model.