Option pricing in a CEV model with liquidity costs

Krzysztof Turek¹

¹ Institute of Mathematics Jagiellonian University 30-348 Kraków, Poland

Applicationes Mathematicae, Tome 43 (2016) no. 1, pp. 25-55

Résumé

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.

Détail

DOI : 10.4064/am2242-1-2016

Keywords: paper make attempt generalise model pricing european options illiquid underlying asset considered rogers singh assume investor decisions have only temporary effect price which proportional square change number asset units investor portfolio assume underlying asset price follows cev model prove existence uniqueness solution techniques similar fixed point theorems feynman kac representation asymptotic behaviour option price small values illiquidity parameter analysed numerical procedure along numerical results included