2020/07/08 by Chinonso Nwankwo, Nwankwo, Chinonso, Weizhong Dai +1 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #65L50 65M50 65N50 #Computational Finance (q-fin.CP) #Differential Equations and Numerical Methods #FOS: Economics and business #Fluid Dynamics and Turbulent Flows #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2007.04408
openalex publication_date 2020/07/08 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method\ncoupled with a fourth-order compact scheme to solve the American put options\nproblem. First, the free boundary problem is converted into a system of partial\ndifferential equations with a fixed domain by using logarithm transformation\nand taking additional derivatives. With the addition of an intermediate\nfunction with a fixed free boundary, a quadratic formula is derived to compute\nthe velocity of the optimal exercise boundary analytically. Furthermore, we\nimplement an extrapolation method to ensure that at least, a third-order\naccuracy in space is maintained at the boundary point when computing the\noptimal exercise boundary from its derivative. As such, it enables us to employ\nfourth-order spatial and temporal discretization with Dirichlet boundary\nconditions for obtaining the numerical solution of the asset option, option\nGreeks, and the optimal exercise boundary. The advantage of the\nRunge-Kutta-Fehlberg method is based on error control and the adjustment of the\ntime step to maintain the error at a certain threshold. By comparing with some\nexisting methods in the numerical experiment, it shows that the present method\nhas a better performance in terms of computational speed and provides a more\naccurate solution.\n