2014/06/04 by Ahmad Reza Yazdanian, Yazdanian, Ahmad Reza, Traian A. Pirvu +1
Economics, Econometrics and Finance · #35K15 #65M06 #91G20 #FOS: Economics and business #FOS: Mathematics #Numerical Analysis (math.NA) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1406.1149
openalex publication_date 2014/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper performs the numerical analysis and the computation of a Spread\noption in a market with imperfect liquidity. The number of shares traded in the\nstock market has a direct impact on the stock's price. Thus, we consider a\nfull-feedback model in which price impact is fully incorporated into the model.\nThe price of a Spread option is characterize by a nonlinear partial\ndifferential equation. This is reduced to linear equations by asymptotic\nexpansions. The Peaceman-Rachford scheme as an alternating direction implicit\nmethod is employed to solve the linear equations numerically. We discuss the\nstability and the convergence of the numerical scheme. Illustrative examples\nare included to demonstrate the validity and applicability of the presented\nmethod. Finally we provide a numerical analysis of the illiquidity effect in\nreplicating an European Spread option; compared to the Black-Scholes case, a\ntrader generally buys more stock to replicate this option.\n