Method of lines for valuation and sensitivities of Bermudan options

TL;DR

This paper introduces a computationally efficient Method of Lines approach for valuing Bermudan options and their sensitivities by transforming PDEs into ODEs, enabling straightforward and fast calculations.

Contribution

The paper presents a novel MOL-based method that simplifies Bermudan option valuation and sensitivities computation by avoiding time discretization and using exponential matrix solutions.

Findings

Efficient pricing of Bermudan options demonstrated

Minimal additional effort needed for Greeks calculation

Numerical experiments confirm accuracy and efficiency

Abstract

In this paper, we present a computationally efficient technique based on the \emph{Method of Lines} (MOL) for the approximation of the Bermudan option values via the associated partial differential equations (PDEs). The MOL converts the Black Scholes PDE to a system of ordinary differential equations (ODEs). The solution of the system of ODEs so obtained only requires spatial discretization and avoids discretization in time. Additionally, the exact solution of the ODEs 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.