Method of Lines for Valuation and Sensitivities of Bermudan Options

Purba Banerjee (), Vasudeva Murthy () and Shashi Jain ()
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Purba Banerjee: Indian Institute of Science
Vasudeva Murthy: TIFR Centre For Applicable Mathematics
Shashi Jain: Indian Institute of Science

Computational Economics, 2024, vol. 63, issue 1, No 10, 245-270

Abstract: Abstract 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.

Keywords: Method of lines; Bermudan options; Fast Greeks; Finite difference method for option pricing (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10614-022-10339-2

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