Applied Mathematics & Information Sciences

Author Country (or Countries)



This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock’s price. Thus, we consider a full-feedback model in which price impact is fully incorporated into the model. The price of a Spread option is characterized by a nonlinear partial differential equation. This is reduced to linear equations by asymptotic expansions. The Peaceman-Rachford scheme, as an alternating direction implicit method, is employed to solve the linear equations numerically. We discuss the stability and the convergence of the numerical scheme. Illustrative examples are included to demonstrate the validity and applicability of the presented method. Finally we provide a numerical analysis of the illiquidity effect in replicating an European Spread option; compared to the Black-Scholes model the price of the option is higher in the model with price impact.

Digital Object Identifier (DOI)