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Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts

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  • Slobodan Milovanovi'c

Abstract

In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. We present a significantly improved RBF-FD scheme and successfully apply it to two types of multidimensional partial differential equations in finance: a two-asset European call basket option under the Black--Scholes--Merton model, and a European call option under the Heston model. We also show that the performance of the improved method is equally high when it comes to pricing American options. By studying convergence, computational performance, and conditioning of the discrete systems, we show the superiority of the introduced approaches over previously used versions of the RBF-FD method in financial applications.

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  • Slobodan Milovanovi'c, 2018. "Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts," Papers 1808.02365, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1808.02365
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    References listed on IDEAS

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    1. Slobodan Milovanovi'c & Lina von Sydow, 2018. "A High Order Method for Pricing of Financial Derivatives using Radial Basis Function generated Finite Differences," Papers 1808.05890, arXiv.org, revised Aug 2018.
    2. 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.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    1. Milovanović, Slobodan & von Sydow, Lina, 2020. "A high order method for pricing of financial derivatives using Radial Basis Function generated Finite Differences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 205-217.

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