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A High Order Method for Pricing of Financial Derivatives using Radial Basis Function generated Finite Differences

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  • Slobodan Milovanovi'c
  • Lina von Sydow

Abstract

In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher accuracy. Still, the discretization matrix is fairly sparse. As a model problem, we consider the pricing of European options in 2D. Since such options have a discontinuity in the first derivative of the payoff function which prohibits high order convergence, we smooth this function using an established technique for Cartesian grids. Numerical experiments show that we acquire a fourth order scheme in space, both for the uniform and the nonuniform node layouts that we use. The high order method with the nonuniform node layout achieves very high accuracy with relatively few nodes. This renders the potential for solving pricing problems in higher spatial dimensions since the computational memory and time demand become much smaller with this method compared to standard techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1808.05890
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    File URL: http://arxiv.org/pdf/1808.05890
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    References listed on IDEAS

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    1. Persson, Jonas & von Sydow, Lina, 2010. "Pricing American options using a space-time adaptive finite difference method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1922-1935.
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    Cited by:

    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.
    2. 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.
    3. Lyu, Jisang & Park, Eunchae & Kim, Sangkwon & Lee, Wonjin & Lee, Chaeyoung & Yoon, Sungha & Park, Jintae & Kim, Junseok, 2021. "Optimal non-uniform finite difference grids for the Black–Scholes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 690-704.
    4. Fazlollah Soleymani & Andrey Itkin, 2019. "Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD method," Papers 1903.00937, arXiv.org.

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