Method of Lines for Valuation and Sensitivities of Bermudan Options

• Published in: Computational economics Vol. 63; no. 1; pp. 245 - 270
• Main Authors: Banerjee, Purba, Murthy, Vasudeva, Jain, Shashi
• Format: Journal Article
• Language: English
• Published: New York Springer US 2024; Springer Nature B.V
• Subjects: Behavioral/Experimental Economics; Computer Appl. in Social and Behavioral Sciences; Discretization; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Efficacy; Exact solutions; Fourier transforms; Math Applications in Computer Science; Mathematical analysis; Method of lines; Methods; Operations Research/Decision Theory; Ordinary differential equations; Partial differential equations; Put & call options; Securities prices; Valuation; Method of lines; Finite difference method for option pricing; Bermudan options; Fast Greeks
• ISSN: 0927-7099; 1572-9974
• DOI: 10.1007/s10614-022-10339-2

In this paper, we present a computationally efficient technique based on the Method of Lines for the approximation of the Bermudan option values via the associated partial differential equations. The method of lines converts the Black Scholes partial differential equation to a system of ordinary differential equations. The solution of the system of ordinary differential equations so obtained only requires spatial discretization and avoids discretization in time. Additionally, the exact solution of the ordinary differential equations can be obtained efficiently using the exponential matrix operation, making the method computationally attractive and straightforward to implement. An essential advantage of the proposed approach is that the associated Greeks can be computed with minimal additional computations. We illustrate, through numerical experiments, the efficacy of the proposed method in pricing and computation of the sensitivities for a European call, cash-or-nothing, powered option, and Bermudan put option.