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Operator splitting schemes for American options under the two-asset Merton jump-diffusion model

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  • Lynn Boen
  • Karel J. in 't Hout

Abstract

This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model. We consider the adaptation of various operator splitting schemes of both the implicit-explicit (IMEX) and the alternating direction implicit (ADI) kind that have recently been studied for partial integro-differential equations (PIDEs) in [3]. Each of these schemes conveniently treats the nonlocal integral part in an explicit manner. Their adaptation to PIDCPs is achieved through a combination with the Ikonen-Toivanen splitting technique [14] as well as with the penalty method [32]. The convergence behaviour and relative performance of the acquired eight operator splitting methods is investigated in extensive numerical experiments for American put-on-the-min and put-on-the-average options.

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  • Lynn Boen & Karel J. in 't Hout, 2019. "Operator splitting schemes for American options under the two-asset Merton jump-diffusion model," Papers 1912.06809, arXiv.org.
    • Handle: RePEc:arx:papers:1912.06809
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    1. Tinne Haentjens & Karel J. in 't Hout, 2015. "ADI Schemes for Pricing American Options under the Heston Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 207-237, July.
    2. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    3. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.
    4. in 't Hout, K.J. & Mishra, C., 2011. "Stability of the modified Craig–Sneyd scheme for two-dimensional convection–diffusion equations with mixed derivative term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2540-2548.
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