آزاده قاسمی فرد

After the financial crisis, market traders realized that a better understanding of the limited liquidity influences on all features of the financial market was needed. One of the origins of such effects is the inclusion of the price impact of option hedging strategies resulting from the relaxation of the assumption of infinite liquidity of the market in underlying assets, which implies that trading affects the price of underlying assets, unlike in Black Scholes markets. Models that incorporate such an effect unavoidably lead to nonlinear feedback. In this talk, we 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 dynamics, 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.