Option pricing in a CEV model with liquidity costs

The goal of this paper is to make an attempt to generalise the model of pricing European options with an illiquid underlying asset considered by Rogers and Singh (2010). We assume that an investor’s decisions have only a temporary effect on the price, which is proportional to the square of the change of the number of asset units in the investor’s portfolio. We also assume that the underlying asset price follows a CEV model. To prove existence and uniqueness of the solution, we use techniques similar to fixed point theorems and Feynman–Kac representation. Asymptotic behaviour of the option price for small values of the illiquidity parameter is also analysed and a numerical procedure along with some numerical results is included.