Azadeh Ghasemifard - University of Mazandaran
Seddigheh Banihashemi - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
Afshin Babaei - Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran.

‎The aim of this paper is to numerically price the European double barrier option by calculating the governing fractional Black-Scholes equation in illiquid markets‎. ‎Incorporating the price impact into the underlying asset dynamic‎, ‎which means that trading strategies affect the underlying price‎, ‎we consider markets with finite liquidity‎. ‎We survey both cases of first-order feedback and full feedback‎. ‎Asset evolution satisfies a stochastic differential equation with fractional noise‎, ‎which is more realistic in markets with statistical dependence‎. ‎Moreover‎, ‎the Sinc-collocation method is used to price the option‎. ‎Numerical experiments show that the results highly correspond to our expectation of illiquid markets‎.

Option pricing, Iliquid market, Sinc collocation method, Price impact&lrm