摘要
This article addresses the problem of pricing European options when the underlying asset is not perfectly liquid.A liquidity discounting factor as a function of market-wide liquidity governed by a mean-reverting stochastic process and the sensitivity of the underlying price to market-wide liquidity is firstly introduced,so that the impact of liquidity on the underlying asset can be captured by the option pricing model.The characteristic function is analytically worked out using the Feynman–Kac theorem and a closed-form pricing formula for European options is successfully derived thereafter.Through numerical experiments,the accuracy of the newly derived formula is verified,and the significance of incorporating liquidity risk into option pricing is demonstrated.
基金
support for a three-year project funded by the ARC(Australian Research Council funding scheme DP170101227)
with which first author’s visiting fellowship was provided for his visit to UoW between Jan 2019 and Dec 2019
support provided by the National Natural Science Foundation of China(No.12101554)
the Fundamental Research Funds for Zhejiang Provincial Universities(No.GB202103001).
