Communications of the
Korean Mathematical Society CKMS

In this paper, we derive the nonlinear equation for European option pricing containing liquidity risk which can be defined as the inverse of the partial derivative of the underlying asset price with respect to the amount of assets traded in the efficient market. Numerical solutions are obtained by using finite element method and compared with option prices of KOSPI200 Stock Index. These prices computed with liquidity risk are considered more realistic than the prices of Black-Scholes model without liquidity risk.

Keywords: stochastic model, option pricing, liquidity risk, finite element method

MSC numbers: Primary 65C20, 65M60, 62P05, 91B28