PRICING AMERICAN OPTIONS WITH THE RUNGE–KUTTA–LEGENDRE FINITE DIFFERENCE SCHEME

Fabien Le Floc’h ()
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Fabien Le Floc’h: Delft Institute of Applied Mathematics, TU Delft, Delft, The Netherlands

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 03, 1-24

Abstract: This paper presents the Runge–Kutta–Legendre (RKL) finite difference scheme, allowing for an additional shift in its polynomial representation. A short presentation of the stability region, comparatively to the Runge–Kutta–Chebyshev scheme follows. We then explore the problem of pricing American options with the RKL scheme under the one factor Black–Scholes and the two factor Heston stochastic volatility models, as well as the pricing of butterfly spread and digital options under the uncertain volatility model, where a Hamilton–Jacobi–Bellman partial differential equation needs to be solved. We explore the order of convergence in these problems, as well as the option greeks stability, compared to the literature and popular schemes such as Crank–Nicolson, with Rannacher time-stepping.

Keywords: American options; stochastic volatility; uncertain volatility; Runge–Kutta–Legendre; Runge–Kutta–Chebyshev; finite difference method; quantitative finance; pricing (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:24:y:2021:i:03:n:s0219024921500187

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DOI: 10.1142/S0219024921500187

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