Numerical analysis for Spread option pricing model in illiquid underlying asset market: full feedback model

摘要

This paper performs the numerical analysis and the computation of a Spreadoption in a market with imperfect liquidity. The number of shares traded in thestock market has a direct impact on the stock's price. Thus, we consider afull-feedback model in which price impact is fully incorporated into the model.The price of a Spread option is characterize by a nonlinear partialdifferential equation. This is reduced to linear equations by asymptoticexpansions. The Peaceman-Rachford scheme as an alternating direction implicitmethod is employed to solve the linear equations numerically. We discuss thestability and the convergence of the numerical scheme. Illustrative examplesare included to demonstrate the validity and applicability of the presentedmethod. Finally we provide a numerical analysis of the illiquidity effect inreplicating an European Spread option; compared to the Black-Scholes case, atrader generally buys more stock to replicate this option.