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Numerical valuation of American basket options via partial differential complementarity problems

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  • Karel in 't Hout
  • Jacob Snoeijer

Abstract

We study the principal component analysis based approach introduced by Reisinger & Wittum (2007) and the comonotonic approach considered by Hanbali & Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.

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  • Karel in 't Hout & Jacob Snoeijer, 2021. "Numerical valuation of American basket options via partial differential complementarity problems," Papers 2106.01200, arXiv.org.
    • Handle: RePEc:arx:papers:2106.01200
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    References listed on IDEAS

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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. Deelstra, G. & Liinev, J. & Vanmaele, M., 2004. "Pricing of arithmetic basket options by conditioning," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 55-77, February.
    3. Griselda Deelstra & Jan Liinev & Michèle Vanmaele, 2004. "Pricing of arithmetic basket options by conditioning," ULB Institutional Repository 2013/7600, ULB -- Universite Libre de Bruxelles.
    4. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    5. Hamza Hanbali & Daniel Linders, 2019. "American-type basket option pricing: a simple two-dimensional partial differential equation," Quantitative Finance, Taylor & Francis Journals, vol. 19(10), pages 1689-1704, October.
    6. Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
    7. Kaas, Rob & Dhaene, Jan & Goovaerts, Marc J., 2000. "Upper and lower bounds for sums of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 151-168, October.
    8. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    9. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.
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