  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 characterize 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 case, a
trader generally buys more stock to replicate this option.
