Abstract
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.
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