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In this paper, we present a computationally efficient technique based on the\emph{Method of Lines} (MOL) for the approximation of the Bermudan optionvalues via the associated partial differential equations (PDEs). The MOLconverts the Black Scholes PDE to a system of ordinary differential equations(ODEs). The solution of the system of ODEs so obtained only requires spatialdiscretization and avoids discretization in time. Additionally, the exactsolution of the ODEs can be obtained efficiently using the exponential matrixoperation, making the method computationally attractive and straightforward toimplement. An essential advantage of the proposed approach is that theassociated Greeks can be computed with minimal additional computations. Weillustrate, through numerical experiments, the efficacy of the proposed methodin pricing and computation of the sensitivities for a European call,cash-or-nothing, powered option, and Bermudan put option.

Method of lines for valuation and sensitivities of Bermudan options