Numerical Schemes and Monte Carlo Method for Black and Scholes Partial Differential Equation: A Comparative Note

Autor:	Sharif Mozumder, Sadia Tasnim, Arafatur Rahman, Abm Shahadat Hossain
Rok vydání:	2015
Předmět:	Hybrid Monte Carlo Mathematical optimization Partial differential equation Successive over-relaxation Iterative method Valuation of options Monte Carlo methods for option pricing Monte Carlo method Applied mathematics Black–Scholes model Mathematics
Zdroj:	Universal Journal of Computational Mathematics. 3:50-55
ISSN:	2332-3043 2332-3035
DOI:	10.13189/ujcmj.2015.030402
Popis:	This paper comparatively investigates some iterative methods and Monte Carlo simulation technique for the dynamics underlying the celebrated Black and Scholes (BS) model. In particular we attempt to answer the question: 'How many Monte Carlo replications can yield prices, for plain vanilla type European derivatives on a stock, which are similar to those obtained by solving the BS PDE using iterative numerical schemes?' We confine to three frequently referred iterative schemes such as Successive over Relaxation (SOR), Gauss-Seidel (GS) and Jacobi (JC). This information together with the information of 'differences in time requirements' will help to guess the similar trade-offs for complex derivatives(exotic) pricing for which there are no analytic pricing formulas.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4e77ae83aa5f256dcf22fb9d55e27d8c https://doi.org/10.13189/ujcmj.2015.030402 Zobrazit plný text záznamu